This research monograph provides a self-contained approach to the problem of determining the conditions under which a compact bordered Klein surface S and a finite group G exist, such that G acts as a group of automorphisms in S. The cases dealt with here take G cyclic, abelian, nilpotent or supersoluble and S hyperelliptic or with connected boundary. No advanced knowledge of group theory or hyperbolic geometry is required and three introductory chapters provide as much background as necessary on non-euclidean crystallographic groups. The graduate reader thus finds here an easy access to...