On the basis of Hua Loo-Keng's results on harmonic analysis on classical groups, the author Gong Sheng develops his subject further, drawing together results of his own research as well as works from other Chinese mathematicians. The book is divided into three parts studying harmonic analysis of various groups. Starting with the discussion on unitary groups in part 1, the author moves on to rotation groups and unitary symplectic groups in parts 2 and 3, providing a survey of harmonic analysis on characteristic manifold of classical domain of first type for real fields, complex fields and quaternion fields.