  This paper grew out of three tutorial lectures on automatic structures given
by the first author at the Logic Colloquium 2007. We discuss variants of
automatic structures related to several models of computation: word automata,
tree automata, Buchi automata, and Rabin automata. Word automata process finite
strings, tree automata process finite labeled trees, Buchi automata process
infinite strings, and Rabin automata process infinite binary labeled trees.
Automatic structures are mathematical objects which can be represented by
(word, tree, Buchi, or Rabin) automata. The study of properties of automatic
structures is a relatively new and very active area of research.
