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This revised fifth edition serves as both a textbook for graduate courses and a reference for researchers who need to use the structure and representation theory of compact groups. Updates address the Bohr compactification of pro-Lie groups, the Lie Theory of Compact Groups with the Exponential Function, and recent work on the theory of weakly complete vector spaces applied to the structure theory of compact groups.

Compact groups. --- Abelian groups, category theory, compact groups, Lie algebra, topological groups.