The contents of this thesis goes back to the year 1979. After two introductory chapters, dealing with so-called short rings and representations of finite groups over such rings, the author arrives at his central themes, such as relative projective modules and non-modular representations and modular representations of cyclic groups. There is a final chapter on Grothendieck groups and Adams operations. As a whole, this work is superseded by the author's papers [in: J. Algebra 72, 478- 500 (1981); ibid. 79, 206-217 (1982)] to which the reader is kindly referred.