Iterated monodromy groups are self-similar groups associated to
partial self-coverings. In my talk I will give an introduction to
iterated monodromy groups of post-singularly finite entire
transcendental functions. These groups act self-similarly on a regular
rooted tree, but in contrast to IMGs of rational functions, every
vertex of the tree has countably infinite degree.
I will also discuss the similarities and differences of IMGs of entire
transcendental functions and of polynomials, in particular in the
direction of amenability. | 
