The Aindra (of Indra) school of Sanskrit grammar is one of the eleven schools of grammar mentioned in Pāṇini's Ashtadhyayi. It is named after Indra in allusion to Lord Indra, the king of Gods in Hindu mythology. Arthur Coke Burnell, a renowned orientologist, in his 1875 book, "On the Aindra school of Sanskrit grammars" details this school. Burnell believed that most non-Pāṇinian systems of Sanskrit grammar were traceable to this school of grammar, believed to be the oldest and reputed to be founded by Indra himself.
Burnell's search for the Aindra school took him to Southern India where he came across the Tamil grammatical work Tolkappiyam. A preface of this work, written during the twelfth century CE by Ilampuranar describes the work as aindiram nirainda Tolkappiyam ('comprising Aindra'). This, Burnell posits is an allusion to the pre-Pāṇinian Aindra school of grammar.
Further, Burnell proceeded to do an exhaustive comparison of the Tokappiyam with two non-Pāṇinian schools of grammar, namely, the Katantra school of Sanskrit grammar and the Kaccayana, a Pali school of Southern India. Based on the comparisons and allowing for divergences due to the structural differences between Tamil and Sanskrit/Pali, Burnell concluded that the Tolkappiyam corresponds to the Katantra school minutely and across the board.
He also demonstrated that many of the technical terms of the Tolkappiyam and of later Tamil grammars were merely simple translations of Sanskrit terms which he attributes to the Aindra school or the other pre-Pāṇinian texts.
While his demonstration of the influence of Sanskrit on the Tolkappiyam has met with some approval, his attribution and approximation of all non Pāṇinian schools of Sanskrit grammar with the Aindra school has met with resistance. Some scholars have also taken a less committal line on the question of Sanskrit influence itself.
Having demonstrated the influence of the Katantra school on the grammars of Pali and Tamil and with the help of a linkage to the Aindra school that the Tolkappiyam afforded, Burnell proceeded to show the differences in the technical terms used by the Aindra school and those used by the Pāṇinians.