Reference for finite state automaton

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I am studying Grigorchuk's groups and it involves somewhat theory from Finite state automatons which I have never had any encounter before. Can somebody suggest me what are the best but self readable reference to it, which also can build up my interest in them as they looked interesting when I googeled.

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For an introductory text, I highly recommend Micheal Sipser's Introduction to the Theory of Computation. It is very accessible, which is probably good if you are going to use it for self-study. The first few chapters are on finite automatons, but it also has sections on further topics like context-free grammars, Turing machines and algorithmic complexity.