An invitation to automata groups

The purpose of this talk is to give a very gentle introduction to the theory of automaton groups and related topics. An automaton group is defined by the action of a Mealy machine on the set of words over a finite alphabet, or by the action via automorphisms on a rooted tree. This class of groups contains groups with exotic and special properties and it has been used to solve open problems or disprove conjectures in several areas of Mathematics. I will present some interesting examples of automaton groups, and their connections with different areas of Mathematics such as Graph Theory, Complex Dynamics and Computer Science.