This book presents an exposition of spherical functions on compact
symmetric spaces, from the viewpoint of Cartan-Selberg. Representation
theory, invariant differential operators, and invariant integral
operators play an important role in the exposition. The author treats
compact symmetric pairs, spherical representations for compact symmetric
pairs, the fundamental groups of compact symmetric spaces, and the
radial part of an invariant differential operator. Also explored are the
classical results for spheres and complex projective spaces and the
relation between spherical functions and harmonic polynomials. This book
is suitable as a graduate textbook.