AMS Chelsea Publishing 1962; 487 pp; hardcover Volume: 341 ISBN10: 0821827359 ISBN13: 9780821827352 List Price: US$57 Member Price: US$51.30 Order Code: CHEL/341.H
 Sigurdur Helgason's Differential Geometry and Symmetric Spaces was quickly recognized as a remarkable and important book. For many years, it was the standard text both for Riemannian geometry and for the analysis and geometry of symmetric spaces. Several generations of mathematicians relied on it for its clarity and careful attention to detail. Although much has happened in the field since the publication of this book, as demonstrated by Helgason's own threevolume expansion of the original work, this single volume is still an excellent overview of the subjects. For instance, even though there are now many competing texts, the chapters on differential geometry and Lie groups continue to be among the best treatments of the subjects available. There is also a welldeveloped treatment of Cartan's classification and structure theory of symmetric spaces. The last chapter, on functions on symmetric spaces, remains an excellent introduction to the study of spherical functions, the theory of invariant differential operators, and other topics in harmonic analysis. This text is rightly called a classic. Sigurdur Helgason was awarded the Steele Prize for Groups and Geometric Analysis and the companion volume, Differential Geometry, Lie Groups and Symmetric Spaces. Readership Graduate students and research mathematicians interested in topological groups and Lie groups; mathematical physicists. Reviews "Remarkably well written ... might be used as a textbook for how to write mathematics."  Bulletin of the AMS Table of Contents  Elementary differential geometry
 Lie groups and Lie algebras
 Structure of semisimple Lie algebras
 Symmetric spaces
 Decomposition of symmetric spaces
 Symmetric spaces of the noncompact type
 Symmetric spaces of the compact type
 Hermitian symmetric spaces
 On the classification of symmetric spaces
 Functions on symmetric spaces
 Bibliography
 List of notational conventions
 Symbols frequently used
 Author index
 Subject index
 Reviews for the first edition
