This book adds to the great body of research that extends back to A. Weil and E. P. Wigner on the unitary representations of locally compact groups and their characters, i.e. the interplay between classical group theory and modern analysis. The groups studied here are the connected Lie groups of general type (not necessarily nilpotent or semisimple). Final results reflect Kirillov's orbit method; in the case of groups that may be nonalgebraic or nontype I, the method requires considerable sophistication. Methods used range from deep functional analysis (the theory of \(C^*\)algebras, factors from F. J. Murray and J. von Neumann, and measure theory) to differential geometry (Lie groups and Hamiltonian actions). This book presents for the first time a systematic and concise compilation of proofs previously dispersed throughout the literature. The result is an impressive example of the deepness of Pukánszky's work. Readership Graduate students and research mathematicians working in topological groups and Lie groups; theoretical physicists. Reviews "The material is very similar to that found in some papers of the author from the early 1970s ... but ... perhaps more structured thanks to the perspective from which the author viewed these matters later ... gives an easier access to the topic than the original papers."  Mathematical Reviews "Apart from many important results which appear for the first time in book form, the present book is a very valuable source for many techniques in the representation theory of general Lie groups. These techniques are beautiful combinations of methods in abstract harmonic analysis and others which are more specific to Lie theory and related coadjoint orbits. [The book is recommended] to everyone interested in general and abstract aspects of the representation theory of Lie groups."  Fachbereich Mathematik "A very valuable source for many techniques in the representation theory of general Lie groups. These techniques are beautiful combinations of methods in abstract harmonic analysis and others which are more specific to Lie theory and related to coadjoint orbits. I can recommend the book to everyone interested in general and abstract aspects of the representation theory of Lie groups."  Zentralblatt MATH Table of Contents  Unitary representations of locally algebraic groups
 Unitary representations of elementary groups
 Existence of characters
 Generalized Kirillov theory
 Bibliography
