This book gives an account of geometric analysis on Riemannian symmetric spaces and its relationship to the representation theory of Lie groups. After discussing the theory of Radon transforms on symmetric spaces, inversion formulas, and range theorems, the book examines applications to invariant differential equations on symmetric spaces, existence theorems, and explicit solution formulas, particularly potential theory and wave equations. It concludes with a chapter on eigenspace representations. Chapter exercises and solutions are included. This second edition further develops the theory of the Fourier transform and the horocycle transform on X, also taking into account tools developed by Eguchi for the Schwartz space S(X). The author received the 1988 Steele Prize for his earlier publications. The book can be used in advanced graduate courses in modern integral geometry, analysis on Lie groups, and representation theory of Lie groups. Annotation ©2009 Book News, Inc., Portland, OR (booknews.com)