this text offers comprehensive coverage of group cohomology, from introductory material through the most recent developments in the field. the primary motivation for this book is the interaction of group cohomology with representation theory, especially the geometry of support varieties over cohomology rings. the appendices, comprising computer calculations of the mod-2 cohomology rings of the groups whose orders divide 64, provide information useful for further developments in the field. a unique feature of this text is that it includes the concepts that are the subject of the calculations and are the source of some of the motivating conjectures for the computations. the programs for computing the cohomology rings were executed in the magma computer algebra language. the text is a valuable resource for researchers in group cohomology and related disciplines. in addition, the book could be used as the text for an advanced graduate class or a graduate seminar.