This book reproduces a course of ten lectures given by the author, Karl W. Gruenberg, at the NSF Regional Conference at the University of Wisconsin-Parkside in July 1974. The aim of the lectures was twofold: to show group theorists how the presentation theory of finite groups can nowadays be successfully approached with the help of integral representation theory, and to persuade ring theorists that here was an area of group theory well suited to applications of integral representation theory. The course was constructed so that only a modicum of either group theory or module theory would be presupposed of the audience. He has also drawn on lectures that he gave at the Australian Summer Research Institute held at the University of Sydney in 1971 and at the Australian National University at Canberra in 1974.