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The correct answer is option 2: Panini.
Option 1: Patanjali - Patanjali is not the author of `Ashtadhyayi`. He is known for his work on meditation and yoga in the text called "Yoga Sutras of Patanjali".
Option 3: Kalidasa - Kalidasa is a renowned Sanskrit poet and playwright but he is not the author of `Ashtadhyayi`. He is known for his works such as "Abhijnanasakuntalam" and "Meghaduta".
Option 4: Banabhatta - Banabhatta is a Sanskrit writer who is famous for his work called "Kadambari", but he is not the author of `Ashtadhyayi`.
The correct answer, option 2: Panini, is the author of `Ashtadhyayi`. Panini is considered one of the greatest grammarians in the history of Sanskrit language. `Ashtadhyayi` is a foundational text that provides a systematic and comprehensive analysis of Sanskrit grammar. It consists of eight chapters (ashta means eight) and is considered a masterpiece in linguistic analysis. Panini`s work in `Asht