Automatic structures are a natural extension of regular languages into algebra. After presenting the formal definition I will show how basic algebraic structures can be realised as automatic structures, and then present some fundamental properties. I will outline more recent research that displays the richness of the area; this involves the classification problem, the isomorphism problem, and the relationship between definability and regularity in automatic structures. The latter results are joint with Bakhadyr Khoussainov, Frank Stephan and Andre Nies.

There are some technical reports available.