Translations of Mathematical Monographs 1991; 259 pp; softcover Volume: 85 Reprint/Revision History: reprinted with corrections 1996, third printing 2001 ISBN10: 0821845446 ISBN13: 9780821845448 List Price: US$99 Member Price: US$79.20 Order Code: MMONO/85
 The first part of this book, which is the second edition of the book of the same title, is intended to provide readers with a brief introduction to the theory of Lie groups as an aid to further study by presenting the fundamental features of Lie groups as a starting point for understanding Lie algebras and Lie theory in general. In the revisions for the second edition, proofs of some of the results were added. The second part of the book builds on some of the background developed in the first part, offering an introduction to the theory of symmetric spaces, a remarkable example of applications of Lie group theory to differential geometry. The book emphasizes this aspect by surveying the fundamentals of Riemannian manifolds and by giving detailed explanations of the way in which geometry and Lie group theory come together. Reviews "The qualities of the book are clear exposition, elegant style of writing, careful selection of material."  Zentralblatt MATH Table of Contents Part I  Concept of Lie group, particularly, linear Lie group
 Compact Lie groups and semisimple Lie groups
 Outline of the theory of Lie algebras
Part II  Riemannian manifolds
 Riemannian symmetric spaces
 Riemannian symmetric spaces of semisimple type
 Hermitian symmetric spaces
