Aṣṭādhyāyī is a really, really old book from India that talks about how words and sentences work together. It was written by a smart man named Pāṇini many, many years ago.
Aṣṭādhyāyī is like a guide or a rulebook for the Sanskrit language. Sanskrit is a language that people used to speak in India a long time ago. The book is very special because it explains how words are made up and how they fit together to make sentences.
Pāṇini figured out that there are only a few basic parts that make up any word. He called these parts "roots" or "bases." It's like building with Legos: There are only a few blocks, but you can use them in different ways to build lots of different things.
Another thing Pāṇini noticed is that words change depending on the situation. For example, you might say "I am happy" if you are feeling good. But if someone asks you "Are you happy?" you would say "Yes, I am." Pāṇini figured out how to change the words so that they fit the situation.
The book is pretty hard to understand because it uses a lot of special symbols and terms. But many people still study it today because it's really important to understanding Sanskrit language and grammar.