This book presents the essentials of harmonic analysis on locally compact groups in a concise and accessible form. The text provides necessary background on Banach algebras and spectral theory, develops the theory of analysis on Abelian groups and compact groups, examines the theory of induced representations, and explores the theory of representations of non-Abelian, non-compact groups. This second edition adds material on representations of the discrete Heisenberg group, coverage of von Neumann algebras and Wiener's theorem, and discussion of SU(2), SO(3), and SO(4) using quaternions.

Gerald B. Folland received his Ph.D in mathematics from Princeton University, New Jersey, USA in 1971. After two years at the Courant Institute of Mathematical Sciences, New York, USA, he joined the faculty of the University of Washington, Seattle, USA, where he is now professor emeritus of mathematics. He has written a number of research and expository articles on harmonic analysis and its applications, and he is the author of eleven textbooks and research monographs.

Banach Algebras and Spectral Theory. Locally Compact Groups. Basic Representation Theory. Analysis on Locally Compact Abelian Groups. Analysis on Compact Groups. Induced Representations. Further Topics in Representation Theory. Appendices.