Essentials of integral geometry in a homogenous space are presented and the focus is on the basic results and applications. This book provides the readers with new findings, some being published for the first time and serves as an excellent graduate text.
The basic properties of convex sets; measures for sets of geometric elements in the plane; fundamental theorems of integral geometry in the plane; applications of integral geometry in the plane; theoretical foundations of integral geometry in a homogeneous space; integral geometry in a euolidean n-space En; applications of integral geometry in En.