This book originated in three lectures given at the Department of Physics and Astronomy, University of Rochester, as Montroll Lectures, on 25, 26 and 30 April, 1990, in honor of the late Professor Montroll. The present expanded version is, however, the result of a special graduate lecture course given by me in the spring semester of 1993. I am greatly indebted to our Department Chairman, Professor Paul Slattery, without whose constant encouragement this book would never have materialized. I am also grateful to Professors Ashok Das and Joseph Eberly for their various assistance in completing and reading the manuscript, and to Ms Judy Mack for a superb typing job. Finally, the book is dedicated to my wife Mary Okubo.

This book is primarily intended for graduate students and researchers interested in mathematical physics. Some knowledge of quantum mechanics and angular momentum algebra at first-year graduate level are required and will be sufficient for understanding most of the material presented in the book, although further acquaintance with Lie algebras in general would be useful.