Euler characteristics are mappings defined on classes of groups and share many common properties with the usual Euler characteristic of finite CW complexes. We are going to see several examples of such mappings defined on various classes of groups as well as ways to calculate the Euler characteristic of groups which split over finite subgroups. In many cases, the Euler characteristic of a group is non-zero and therefore we obtain information about the isomorphism classes of subgroups. In this direction, we see also applications for self maps of manifolds. Speaker(s): Konstantinos Tsouvalas (UM)