The book is a continuation of the second book, presenting more recent material. It treats Radon transforms for various double fibrations, the main example being the sets of points and of horocycles in a symmetric space (p.145). Later chapters deal with a geometric Fourier transform on symmetric spaces (noncompact and compact) and range theorems for Radon and Fourier transforms with applications to differential equations. The final chapter deals with eigenspace representations associated with homogeneous spaces. The first book contains a complete table of contents.