This book contains the author's notes for a course that he taught at ETH, Zürich. The aim is to lead the reader to a proof of the PeterWeyl theorem, the basic theorem in the representation theory of compact topological groups. The topological, analytical, and algebraic groundwork needed for the proof is provided as part of the course. A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels. Readership General audience interested in the PeterWeyl theorem. Reviews "The presentation in this text is clear and to the point. The methods used are good classical ones. This is a good text for a student who knows little about locally compact groups and wants to get an introduction to some of the fundamental ideas needed to begin the study of them."  Mathematical Reviews Table of Contents  Topological preliminaries
 The Haar measure on a locally compact group
 Hilbert spaces and the spectral theorem
 Compact groups and their representations
