An introduction to group-theoretic methods on spaces with symmetry given by the action of a Lie group. An introductory chapter offers a self-contained account of the analysis on surfaces of constant curvature. Later chapters cover general cases of the Radon transform, invariant differential operators, invariants and harmonic polynomials, spherical functions and spherical transforms, and analysis on compact symmetric spaces. Helgason was awarded the Steele Prize for outstanding mathematical exposition for this work. Annotation c. Book News, Inc., Portland, OR (booknews.com)