Fixed Rings of Finite Automorphism Groups of Associative Rings 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.