This book presents an account of the theory of the cohomology ring of a finite group. The aim is to present a modern approach from the point of view of homological algebra, and the volume covers themes such as finite generation theorems, the cohomology of wreath products, the norm map, and variety theory.Prerequisites comprise a familiarity with modern algebra and homological algebra as might be gained from introductory graduate courses, though otherwise the book is self-contained. As a result, the book will be useful for those already engaged or commencing in research in this area of mathematics by providing an up-to-date survey of important techniques and their applications to finite group theory.

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