Samskritam Notes: Classification of Letters

(This article requires you to have some basic knowledge of Samskritam and uses Devanagari script in between)

Panini’s Ashtadhyayi

I don’t know if grammarians of any other language have analyzed the letters of a language like Samskritam grammarians. Samskritam letters have been classified in many ways — from where the sound originates in the mouth to the amount of breath involved to the effort involved in saying the letter. In this post, I want to go over classifications based on length, tone, and nasalization.

In Samskritam, like most languages, there are vowels and consonants. In most Indian languages, they are kind of similar. For example, here are the Malayalam vowels. If you read the transliteration below the letter, you will find that your mother tongue has identical letters.

Malayalam Vowels

When it comes to Samskritam, the vowels are represented in the Maheshwara Sutras by the pratyahara अच् (See The brilliance of Panini). If you expand, अच्, you get the following letters: अ इ उ ऋ लृ ए ऎ ओ औ. There are just 9 letters.

The first letter is pronounced as “a” in both Malayalam and Samskritam. While Malayalam has “a” and “aa,” Samskritam has only “a.” Does it mean that Samskritam does not have a long a.?

In Samskritam, if you pick one of the vowels, it does not represent that single character but much more. For example, take the letter “a.” It’s not just one letter. It encompasses many different letters.

There are three different classifications of vowels, and they are based on

  • length (it can be short, regular, or long)
  • tone (there are three different tones or pitches at which you pronounce the letter)
  • nasalization (a letter can be said in a usual way and also in a nasalized way)


Each vowel can be pronounced as either hrasva (ह्रस्व), deergha (दीर्घ ) or plutha ( प्लुत). Let’s say someone is mentioning the person named Krishna. They could say Krishna with a short ending and not elongating the end. That would be ह्रस्व or short. If they are calling on Latha, the ending “a” is long or दीर्घ. Now let’s say Krishna is far away in the field, and Yashoda calls him “Krishnaaa” with an elongated “a” for three beats. That would be a प्लुत. When you write a प्लुत letter, you put the number 3 next to it, to indicate that it should be elongated for three beats. Technically, ह्रस्व is of one matra of time, दीर्घ is two and प्लुत three.

If you put it into a table, it will look like this.

अ ३
इ ३
उ ३
ऋ ३
ऌ ३
ए ३
ऐ ३
ओ ३
औ ३
Samskritam Aksharaprakaranam

As you can see, not all letters have all the variations.

  • लृ does not have a दीर्घ.
  • ए does not have a ह्रस्व. It starts off as दीर्घ
  • ओ, ऐ and औ does not have have ह्रस्व either.

The take away from this section is that, when you refer to the vowel अ, it refers to the three variations of अ, which are the ह्रस्व दीर्घ and प्लुत variations.

That’s not it.


Take the letter अ. You can utter it in a higher pitch, normal pitch, or low pitch. These three pitches are called उदात्त, अनुदात्त. and स्वरित

  • उदात्त is a higher pitch
  • अनुदात्त is a lower pitch
  • स्वरित happens when the उदात्त and अनुदात्त are combined, and you get the middle sound.

This is hard to explain verbally. So here are two videos where Vedic scholars demonstrate this concept. I visualize this as a sine wave. The उदात्त is the crest, अनुदात्त is the trough and स्वरित is the base.


Finally, you can utter a letter with a nasal sound or in a non-nasalized form.

These are referred to as

  • अनुनासिक (nasalized)
  • अननुनसिक (non-nasalized)

If you look at the अ mentioned in the Maheshwara Sutras, you can see that it has all these forms. If you take अ, it can have 3 lengths (ह्रस्व, दीर्घ, प्लुत), 3 tones(उदात्त, अनुदात्त, स्वरित), and 2 (अनुनासिक, अननुनसिक). Thus अ can have 18 forms. That is true for अ इ उ and ऋ. The remaining letters do not have three lengths. Hence they will only have 12 forms. So when you chant the Maheshwara Sutras, you should know that they have all these forms.

Who has ever thought about letters this way? Classifying and categorizing them in so many different ways.


  • संधिःby महबलेश्वरभट्ट्:
  • Lecture by Sri Varun Khanna at Chinmaya International Foundation

Samskritam Notes: Understanding a sloka

(Even if you don’t understand, Samskritam, you can read through and understand the logic)

Take a look at this verse from Valmiki Ramayanam

इक्ष्वाकुवंशप्रभवो रामो नाम जनैश्श्रुत:
नियतात्मा महावीर्यो द्युतिमान्धृतिमान् वशी

When you first look at this verse, it appears incomprehensible with long words. Fortunately, there is a well-defined step by step process which will split the words apart and help us comprehend the meaning. The actual process followed by Samskritam students has more steps, but I am compressing it just to demonstrate the effectiveness of the process. What makes the verse look intimidating initially is the use of concepts like sandhi and samasa, which joins words to form compound words. This process reverses it, like running a film in reverse.

1. पदच्छेदः or splitting of the words.

This is the step where you break up joined words into their individual parts. In Chemistry, when you are given NaCl, you know that it is made up of Na and Cl. In Samskritam, words are joined using sandhi rules and in this process, you reverse that. To do this, you need to know the sandhi rules, but follow along and you will get it.

इक्ष्वाकुवंशप्रभवः रामः नाम जनैः श्रुतः
नियतात्मा  महावीर्यः द्युतिमान् धृतिमान् वशी

In the verse it was इक्ष्वाकुवंशप्रभवो रामो, but now it has become इक्ष्वाकुवंशप्रभवः रामः by reversing a visarga sandhi. Similar changes have been applied in other places as well.

2. आकाङ्क्षा or inquiry

In this process, you first find the verb in the sentence. Then you keep on asking questions till you cover all the words in the verse.

The verb in this verse is श्रुतः which means was known or was famous. You note it down


The next question would be, among whom?

Q: कैः श्रुतः

A: जनैः श्रुतः (he was known among the people)

Next question would be: what was known or famous among the people?

Q: जनैः किं श्रुतः जनैः

A: रामः नाम जनैः श्रुतः (the one by the name of Rama was known among the people)

Next question would be, what kind of person was this Rama, who was known among the people?

Q: जनैः कीदृश रामः नाम श्रुतः

A: जनैः इक्ष्वाकुवंशप्रभवः रामः नाम श्रुतः (the one born in Ikshvaku dynasty was the Rama known among people)

next question is: again, what kind of person was this Rama, who was known among the people?

answer: जनैः इक्ष्वाकुवंशप्रभवः नियतात्मा रामः नाम श्रुतः (the one born in Ikshvaku dynasty and one who has control of his aatma was the Rama known among people)

You keep on asking the above question again and again and finally you get this

इक्ष्वाकुवंशप्रभवः नियतात्मा महावीर्यः द्युतिमान् धृतिमान् वशी रामः नाम जनैः श्रुतः

Finally, we have poetry converted to prose by this process.

The final step is to find alternate words to the ones above so that the sentence can be simpler in meaning. It will be then in your own words.

Word in VerseDifferent Word in SamskritamMeaning
इक्ष्वाकुवंशप्रभवःइक्ष्वाकु-कुले प्रसूत:Born in Ikshvaku dynasty
नियतात्मास्ववश: आत्माself controlled
 महावीर्यःमहाशूरःvery powerful
वशीजितेन्द्रियःone who has conquered sense organs
रामः नामरामः इति नामby the name ‘Rama’
जनैःनरैःby common men

Now you can write in your own words the following sentence

इक्ष्वाकु-कुले प्रसूत: स्ववश: आत्मा महाशूरः कान्तियुक्त: स्थिरचेतसः जितेन्द्रियः रामः इति नाम नरैः ज्ञातः

There is one descended in the line of lksvaku and known by men by the name of Rama. He has fully controlled his mind, very powerful, radiant and resolute has brought his senses under control.

Simple, isn’t it?

Sanskrit Notes: Order of Words

Rudraksha by Kinshuk Sunil (flickr
Rudraksha by Kinshuk Sunil (flickr)

One of the interesting features of Sanskrit is that, in a sentence, the order of the words don’t matter. You can switch them around and the meaning remains the same.
Take for example a sentence like, Rama is going to the forest. You can’t say, “Rama going forest.” You need the “is” and “to the” to make sense of the sentence. The “is going” indicates that it is one person who is doing the action. Now, “to the forest” indicates that the forest is the object of the action.
In simple Sanskrit, you would write it like this
रामः वानमं गाच्छति
It reads, “Ramah vanam gachati”,  When you say “Ramah”, it indicates one Rama. A forest is “vana”, but in the sentence, we wrote it as “vanam”. That indicates, it is the object of Rama’s destination. The “ti” at the end of “gacchati” indicates that it is one Rama who is going (not two)”. If there were many Ramas, it would have become “gacchanti”. Thus the “is going” and “to the” are built into the words themselves.
This makes it interesting. Now you can write

  • गाच्छति रामः वानमं
  • गाच्छति वानमं रामः
  • वानमं गाच्छति रामः

All these sentences mean the same even though the order of words are switched around. Since each word has the part which maintains its relationship to the verb, the order does not matter. Due to this, in poetry, you can switch words around to fit the meter. In Hindu tradition, almost everything is written in poetry form and this made it easier for an oral society to remember anything forever.
Here is a complicated sentence
भारत ! यदा यदा धर्मस्य ग्लानिः अधर्मस्य अब्युधानं च भवति तदा अहम् आत्मानं सृजामि
Take those words and resequence them and apply the sandhi rules, and you get the following verse from chapter 4 of Gita

यदा यदा हि धर्मस्य ग्लानिर्भवति भारत ।
अभ्युत्थानमधर्मस्य तदात्मानं सृजाम्यहम् ॥४-७॥

Here is an exercise. Try the “Rama is going to the forest” in your mother tongue and see how it behaves. Does it work the same in Dravidian languages and Indo-European languages? In Malayalam, it behaves exactly the same as in Sanskrit. In Hindi, it does not.

  • Based on the lectures of Varun Khanna at Chinmaya International Foundation
  • Gitapravesha by Samskrita Bharati

Three Stage Evolution of Mahabharata – jayam, bharatam, mahabharatam

Mahabharata (via Wikipedia)
Mahabharata (via Wikipedia)

There are clues in Mahabharata which tells us about how the itihaas grew to become the longest poem with over a lakh verses. Mahabharata is divided into 18 parvas with Harivamsha as the 19th. The core of it — around 24, 000 — verses are about the war between the Pandavas and Kauravas. Besides this, there are tales of gods, kings, sages, discourses on philosophy, religion, law and various asramas of life. We know that Vyasa was the composer who taught it to Vaisampayana who then narrated it to Janamejaya at his sarpa yagna. Ugrasravas, the suta, then narrated it to others at Namisharanyam. Recently I read a book — A short history of Sanskrit Literature — which elaborates on a theory on how Mahabaharatam came to be.
Here are three verses from Mahabharata which refers to three different lengths

  • This verse refers to the first stage that has over 8000 verses
    Mahabharata - Reference to ashtau shloka sahasrani or 8000 shlokas
    Mahabharata – Reference to ashtau shloka sahasrani or 8000 shlokas
  • This is the reference to the 24,000 verses
    Mahabharata - chatur vimshati sahasrim - or 24,000 verses
    Mahabharata – chatur vimshati sahasrim – or 24,000 verses
  • This is the reference to the third stage that has over a lakh verses.
    Mahabharata - shata sahasram or 100, 000 shlokas
    Mahabharata – shata sahasram or 100, 000 shlokas

It is not just that the number of verses increased; the name of the itihaas changed as well. The very first line in adi parvam refers to it as jayam.

नारायणं नमस्कृत्य नरं चैव नरॊत्तमम
देवीं सरस्वतीं चैव ततॊ जयम उदीरयेत

Then it became bharatam and finally mahabharatam. Was it because it passed through three people — Vyasa, Vaisampayana, and Ugrasravas?

A short history of Sanskrit Literature, by TK Ramachandra Aiyar
A short history of Sanskrit Literature, by TK Ramachandra Aiyar

The author of the book, T. K. Ramachandra Aiyar, thinks that the core of Mahabharata is the rivalry of Kurus and Panchalas. Their enemosity is historic. They quaralled for a long time and finally there was a union. The Yajurveda — which was composed in a nearby region — mentions this. The Kathaka Samhita, though speaks of a dispute between Vaka Dalbhya from Panchala and a Dritharashtra who is the son of a Vichitravirya, a Kuru. Over time, the kingdoms split again and engaged in constant rivalry. By the time of Mahabharata, the Kuru and Panchala kingdom were separate.
Prior to the war, there was a turn of events which caused the annexation of Northern Panchala by the Kurus. This is the incident, where Drona defeats Drupada using Arjuna. This event upset the balance of poweer between the two kingdoms. The Kurus were defeated in the war and the Panchalas won along with the Pandavas. (Here is an interesting explanation about the Mahabharata war, not as a rivalry between Kauravas and Pandavas, but as a war between Kurus and Panchalas).
With this background, here is the theory on what might have happened. The defeat of the Kurus would have resulted in various songs glorifying the victory of the Pandavas and their allies. Sutas would have sung this in various assemblies. This would have been Jayam. By the second stage, when it reaches 24,000 verses, the life of Pandavas was elaborated. Krishna was represented as an incarnation of Vishnu and Shiva and Vishnu become more prominent than Brahma. The epic became popular all over bharatavarsha and other additions like the stories of gods and sages were added and it became a treatise on dharmashastra. This was the third stage.
The book became an authority on dharma dealing with religion, law and morality. It was accorded the status of the 5th veda. There are land grants dating between 462 CE and 532 CE, which talks about the one-lakh verse Mahabharatam compiled by Vyasa. There are numerous literary evidence from Sanskrit authors on the stature of Mahabharata. From Ujjayini to Khamboja, the ithihaas was read in temples. It became a national epic.

The Paninian Prakriya

(It is recommended that you read The brilliance of Panini before this article)

Panini's Ashtadhyayi
Panini’s Ashtadhyayi

रामः पठति – Rama studies. If it happened in the past, you would say, रामः अपठत् and if it is going to happen in the future, it would be रामः पठिष्यति. You can see the transformations of the word पठ and you would think that is the root word. According to Panini, the root is पठं. That is the dhatu or the verbal root. That root has some extra attachments which is then transformed through a set of operations, which we can call a Paninian Prakriya, to the commonly used form. We don’t use all the letters in a dhatu while speaking or common usage and so the dhatu has to be cleaned up.
Given that there are around 1943 dhatus, how do you come up with rules that can be applied  to derive the common form? That’s where you see the brilliance of Panini, who built on top of the work of other grammarians. Paninian grammar is the only complete, explicit, rule-bound grammar of any human language and studying this grammar gives insight into the mind of our rishis.
To give concrete examples of how the Paninian prakriya works, let’s look at a set of rules called it-saṁjñā. As we saw, the dhatu has a bunch of extra additions and they need to be cleaned up. In it-saṁjñā, Panini specifies a sequence of rules which are applied to the dhatu. Each rule attaches a flag to certain letters in the dhatu. Once you run through all the rules, the last rule says, drop all the letters that have been marked. With this, the dhatu is cleaned up.

Few rules of it-saṁjñā

Here we will look at few of the rules and use simple examples. Once these are laid out, we will use some complex examples and see how they all connect as an algorithm. If you don’t get these concepts, it’s fine. How all these play together will be explained in the final section.
Rule 1: उपदेशेऽजनुनासिक इत् It means that any vowel that is nasalized, gets it-saṁjñā For example, take the dhatu धूपँ and split the words as ध् ऊ प् अँ. In this list there is a nasalized vowel, and it is अँ, so the अँ gets the it-saṁjñā. Think of it as underlining the अँ with a red color marker for now.
Rule 2: हलन्त्यम् This means that if there is a consonant (hal) that is at the end (antyam) then it gets the it-saṁjñā. To take an example, इङ् can be split into इ ङ् and since ङ् is a consonant, it gets the it-saṁjñā. What remains is इ. Also take a look at the प्रत्याहारः rules  to see what hal means.
Rule 3: न विभक्तौ तुस्माः means that there is an exception to rule #2. This rule falls into a category known as उत्सर्ग-अपवादः  The rule says, yes, you can drop the consonant as per rule #2, except when the consonants are त्, थ्, द्, ध्, न्, स्, or म् (the expansion of तुस्माः) or is the end of a विभक्ति . Take the word तस् = त् अ स्. Due to rule #2, स् should be dropped. But स् is at the end of विभक्ति प्रत्यय and hence is not marked as it-saṁjñā.
Rule 4: आदिर्ञिटुदवः ञि, टु, and डु (ञिटुडवः) are marked as इत् if it is at the beginning (आदिः) Take the dhatu डुदाञ् = ड् उ द् आ ञ्.  Here डु receives the इत्-संज्ञा by this rule.
Rule 5: षः प्रत्ययस्य The letter ष् (षः) found at the beginning (आदिः) of a प्रत्यय  is given the marker इत्. For example, in षाकन् = ष् आ क् अ न् , the first letter ष् receives the इत्-संज्ञा.
Rule 6: चुटू The letters च्, छ्, ज्, झ्, ञ्, ट्, ठ्, ड्, ढ्, or ण् (चुटू) found at the beginning (आदिः) of a प्रत्यय are marked इत्. For example, in णिच् = ण् इ च्. Here ण् receives the इत्-संज्ञा because of this rule.
Rule 7: लशक्वतद्धिते The letters ल्, श्, क्, ख्, ग्, घ्, or ङ् found at the beginning of a प्रत्यय, but not at the beginning of a तद्धित प्रत्यय are marked इत्
Running the above the rules underlines various letters for इत्. The last rule is like the garbage collector in programming languages. It finds all those marked letters and drops them.
Rule 8: तस्य लोपः — All those elements that received the marker इत् (तस्य) disappear (लोपः)

Examples with explanations

Now that we know all the rules, it would help to take some examples and run them through this sequence and see the transformation of a dhatu.

  1. णमुँल् – Breaking down into individual letters, you get ण् + अ + म् + अँ + ल्  Now apply rule #1 and since there is a nasalized vowel (अँ), mark it with red color. Then go down the list of rules and see which one matches.  The next one that matches is #2 and mark ल्  with a red color marker. Scan through the rule set and we find that #6 applies as well. So we mark ण्  with our marker. No other rule applies here and so we come to rule #8 which says, drop all those letters which were marked. Doing that gives us अम्
  2. ञिष्विदाँ – Breaking down that again, you get ञ् + इ + ष् + व् + इ + द् + आँ . Going through the rule set, rule #1 applies you we mark आँ with a marker. Then going down, we find that rule #4 also applies, marking ञ. Finally, we come to rule #8 and drop those two letters leaving us with ष्विद्
  3. Let’s do one more. ध्वम्. This breaks down into ध् + अ + व् + म्. Rule #2 applies here and we mark म्. Then the third rule kicks in and says, hold on. You cannot mark it and so we are left with  ध्वम् itself.

The grammarians of India looked at Sanskrit used in scripture and for speaking and then came up with the grammar which was used to build up the rules. The it-saṁjñā is just one of the many such rules.
There is one question though. If you are using the word पठ, then why bother writing it as पठं. and then apply all these rules to drop few characters. That is a topic for another post.


  1. Based on the lectures by Varun Khanna at Chinmaya International Foundation and my Sanskrit teachers.
  2. Taking धूपँ and splitting up it into ध् ऊ प् अँ is called anupurvi
  3. The dhatu णमुँल् is called sa-anubandha dhatu and the cleaned up version अम् is called the niranubandha dhatu

Sanskrit Notes: Context

Wise Principle
Wise Principle

(This is the translation of a story which appeared in Sambhashana Sandesha magazine. The translation is mine)
Once upon a time, a pundit went to the river to take a bath. While taking bath, he uttered a shlokam, which meant the following
“The love of a mother is the greatest, so is the strength of the brother.
The light of the sun is the best, so is the water from Ganga.”
A washerwoman, who was listening to this started laughing. Feeling insulted by her laughter, the pundit complained to the village chief, who summoned the woman and asked, “Why did you insult the pundit?”
The woman replied, “I did not insult him”
The pundit got angry, “Didn’t you laugh listening to my shlokam? Isn’t that insulting me?”
“Of course I laughed. That’s because your shlokam is laughable”
The pundit asked, “Isn’t the affection of a mother great? Isn’t the strength of the brother great? Isn’t the rays from the sun, bright? Isn’t the water from Ganga holy?”
The woman replied, “Sure, all those are excellent. But there are other principles, which are better. For example, if there is a fight between the father and son, the mother will support the father. At that time he would find the love of his wife the greatest.
Another example: if an enemy is attacking me, the strength of my shoulders would be the best defense.
If my eyes are weak, then I could become blind. Then the rays of light entering my eyes would be the best.
If there is drought, then life would get miserable. Then if it rains, that water would be the best.”
Everyone admired the wisdom of the washerwoman.
Thus, everything depends on the context.

Sanskrit Notes: Tenses

Learning Sanskrit by Avanish Tiwary (Flickr)
Learning Sanskrit by
Avanish Tiwary (Flickr)

Like any language, Sanskrit has the three tenses: the present, past and future. They are called वर्तमानकालः, भूतकालः and  भविष्यत्कालः respectively. For the present tense, there is just one way of saying it. In Sanskrit grammar, it is called लट् लकार.
When we look at the past and the future it gets interesting. There is more than one way of representing the future or there are two लकार.

  1. लृट्- Commonly used for future tense
  2. लुट् – is used to represent अनद्यतन events which means any event that did not happen today. Used to refer to events happening tomorrow and after. Thus technically you cannot say,रामः  शवः वनं गमिष्यति. The correct version is रामः  शवः वनं गन्ता

When it comes to the past, there are three ways

    1. लङ्घ् – अनद्यतन भूतकालम means, the event did not happen today.
    2. लुङ्ग् – Used commonly
    3. लिट् – It happened, but I did not see it with my own eyes


The brilliance of Panini

Long time back in Takshashila, there lived two students who were studying to be grammarians,  a popular topic. One of them was dull; the other very bright. Everyone used to make fun of the dull boy and drummed into his head that he would amount to nothing in this world. Despite all that negativity, he studied to be a  vayyakarana, which was a big deal. The other boy was brilliant and was favored by the teachers.
One day, fed up with all the taunting, the dull boy left went to the forest and started meditating on Shiva. It is said that after a long time, he got blessed or got some insights. A version of the events says that he heard the sounds of the damaru played it 14 times. Instead of the beats of the damaru, the boy, who was focussed on grammar heard sounds as follows.

  1. अ इ उ ण् |
  2. ऋ ऌ क् |
  3. ए ओ ङ् |
  4. ऐ औ च् |
  5. ह य व र ट् |
  6. ल ण् |
  7. ञ म ङ ण न म् |
  8. झ भ ञ् |
  9. घ ढ ध ष् |
  10. ज ब ग ड द श् |
  11. ख फ छ ठ थ च ट त व् |
  12. क प य् |
  13. श ष स र् |
  14. ह ल् |

These 14 sutras — Maheshwara Sutras — became the basis for the text Ashtadhyayi (the text with 8 chapters) which codified the rules of  Sanskrit, both spoken language (laukika) and the compositional language (vaidika). Due to the perfection achieved by the boy, Panini, Indian linguistic thought can be divided into pre-Panini and post-Panini eras.
Panini was not the first one to attempt this feat. Ashtadhyayi mentions others before him. But, Panini’s codification was so perfect that it superseded other prevalent grammars. Well, almost perfect. Katyana or Vararuchi who was the brilliant kid wrote a commentary on Ashtadyayi called vartika sutras, in which he criticized the Ashtadyayi. Later, Patanjali came along and combined the vartikas with the Ashtadyayi and wrote the mahabhashya.

We constantly hear that what Panini achieved was a great feat of human intellect. To appreciate Panini even further,  we have to understand some of the concepts he introduced and how those help in codifying grammar concisely. At a high level, he came up with a number of primitive elements and derived the infinite number of actual forms of words in use. It uses concepts like the definition, compressing large amounts of data,  defining the steps of an algorithm with a terminating condition, and condensing text without losing information. The grammars that are common are paradigmatic. In this, you learn the finished product. For example, if you take the word Ramah in Sanskrit and write the ekvachan, dvi-vachan and bahu-vachan, you get ramah, ramau, ramaah. Panini’s grammar tells you how to derive ramah, ramau, ramaah.
I will illustrate some of the grammatical tools of  Ashtadhyayi using examples so that we all can appreciate the work of Panini and the grammarians who preceded and followed him.


In our life, we are used to abbreviations. When we go to the bank,  instead of saying Demand Draft, we say DD. Instead of saying television, we say TV. A similar concept is introduced by Panini called प्रत्याहारः
प्रत्याहारः  is simply a way of naming a sequence of words. To take an example, अच्. means all letters starting with अ and ending in च्. Let’s go to the Maheshwara Sutra and start with line 1. It starts with अ. Now keep going till you encounter a च्. You find that as the last character on line 4. Now get all the characters from अ toच् (excluding च् ) and you have all your swaras. Thus instead of saying swaras, you say अच्.  
This technique helps condense large information into a small number of letters. If you look at Maheshwara Sutras and the number of possibilities, you can make up a large number of pratyaharas. All you need to do is pick a starting letter and an ending letter. But in fact, only 44 are considered pratyaharas (Panini used 42 in Ashtadyayi)
Now that we have the concept of प्रत्याहारः, let’s see how it is used
In Sanskrit, words ending in swaras are called ajanta. 
अजन्तः = अच् + अन्तः
This means that any word ending (अन्तः) in अच् is  a swara.  Since we defined what अच् is, अजन्तः makes sense.
To see a more complicated example, take the following sutra
इको यण् अचि
Take the first word इको,  which means ‘of इक्’.  Again, look up the Maheswara Sutras and find all the letters that start at इ  and end at क् . Thus you get the following इ उ ऋ ऌ (All the letters at the end of the line are dropped and that’s why we don’t list ण् or क्). The second word यण् lists all the following letters य् व् र् ल्.
The rule is used in यण् संधि. It says, when you encounter इ उ ऋ ऌ, they are replaced by य व र ल respectively. Or in a tabular form, it would look like this


To see an example, let’s look at प्रति  + एकः = प्रत्येकः
This would be प्र + त् + इ + ए + कः . Based on the table above इ would becomeय्, thus making प्रत्येकः
Let’s take another rule एचोयवायाव:
Splitting this, you get एचः  अय अव आय आव. Using the Maheswara Sutras, you find एचः and get ए ओ ऐ औ. Applying the rest of the rules you get a tabular form like this


Thus what you get is an algorithm or prakriya  (प्रक्रिया).  In the West, they think algorithms started with Euclid and was formalized by Church and Turing at Princeton in the 1930s.


The process of naming something is called संज्ञा. Every scientific field has technical terms.  These are technical terms that will be used in Ashtadyayi. The best example is the first sutra in Ashtadyayi.
वृद्धिः  आदैच्.  
This says that the letters in आदै will be called वृद्धिः Once  वृद्धिः is defined, it can be used in other sutras. Another example is १.४.३ यू स्त्र्याख्यौ नदी । Here नदी is defined as ee-karantha and uu-karanatha streelinga words.
It is best to think of these as aliases. There are 91 संज्ञा  in Ashyadyayi and about 66 of them are defined in the first chapter.


This is the technique based on which Ahstadyayi has been built. When a concept is taught, first the most basic sutra is given. He will then follow it with all the exceptions to that rule.
Let’s look at an example
३.१.६८ कर्तरि शप् ।
३.१.६९ दिवादिभ्यः श्यन् ।
These two follow one after the other. The first one is the basic concept or उत्सर्ग. He then follows it with the exception rule saying, but if it is in दिवादि gana, then here is the exception rule or अपवादः (Don’t worry too much about what is a दिवादि gana)
So taking the basic rule, we have पठ + शप् + ति  = पठति
And the exception rule = नृत् + श्यन् + ति = नृत्यति (Because it is in the दिवादि gana)
Thus again, the algorithm or प्रक्रिया is followed here. You would take the word नृत् and try to apply the उत्सर्ग rule. Then you realize, it belongs to the दिवादि gana and hence you need to apply rule #2. Once you are done with that, the प्रक्रिया terminates. At the same time, if you pick पठ, you know that it does not belong to दिवादि gana. So the first rule is applied and the प्रक्रिया  terminates.


This is tied to the concept of उत्सर्ग-अपवादः. Anuvritti is a part of a previous sutra that is carried to the sutras that follow it immediately. An example will make it clear.
७.१.२३ स्वमोर्नपुंसकात् ।
७.१.२४ अतोऽम् ।
This is an example of उत्सर्ग-अपवादः. The first sutra is a general rule for all napumsaka lingas. It says that in napumsaka, सुं or अम्  gets removed and hence वारि remains as वारि
But this does not work for words like फलम् which are a-karantha pullinga.  So it becomes फल + अम्  = फलम्  Here the second sutra is the अपवादः sutra which talks about the exception.
Now, look at the अपवादः rule. The word नपुंसक is not repeated. It is invisible but is required. This concept is अनुवृत्तिः  
To give another example, there is a sutra called इको यण अचि. The second sutra is called एचोयवायाव:. Here the अचि is implied.
Panini does not repeat anything. It helps remove unnecessary repetitions and condense the sutras. Words are removed, but the information that is essential is conveyed.
These are just a few concepts used in Ashtadyayi. There are many others which I have left out.  At an initial glance, these sutras appear terse, dense, allusive and mysterious, but once they are unlocked, they cast a brilliant light on the power of Panini’s mind.