"This book contains written versions of the lectures given at the PCMI Graduate Summer School on the representation theory of Lie groups. The volume begins with lectures by A. Knapp and P. Trapa outlining the state of the subject around the year 1975, specifically, the fundamental results of Harish-Chandra on the general structure of infinite dimensional representations and the Langlands classification.". "Each contributor to the volume presents the topics in a unique, comprehensive, and accessible manner geared toward advanced graduate students and researcher. Students should have completed the standard introductory graduate courses for full comprehension of the work. The book would also serve well as a supplementary text for a course on introductory infinite-dimensional representation theory."--BOOK JACKET.