Table of Contents

Preliminaries.- Rings with no |G|-torsion: Existence of fixed elements, the prime radical and Jacobson radical of RG.- Simple rings: Inner and outer automorphisms, simple fixed rings, R as an RG-module.- Inner and outer automorphisms of semiprime rings.- Rings with no nilpotent elements: Existence of fixed elements and traces.- Chain conditions.- Polynomial identities.- Skew group rings and applications to modules.