  The theory of iterated monodromy groups was developed by Nekrashevych. It is
a wonderful example of application of group theory in dynamical systems and, in
particular, in holomorphic dynamics. Iterated monodromy groups encode in a
computationally efficient way combinatorial information about any dynamical
system induced by a post-critically finite branched covering. Their power was
illustrated by a solution of the Hubbard Twisted Rabbit Problem given by
Bartholdi and Nekrashevych.
  These notes attempt to introduce this theory for those who are familiar with
holomorphic dynamics but not with group theory. The aims are to give all
explanations needed to understand the main definition and to provide skills in
computing any iterated monodromy group efficiently. Moreover some explicit
links between iterated monodromy groups and holomorphic dynamics are detailed.
In particular, combinatorial equivalence classes and matings of polynomials are
discussed.
