This unique book develops the classical subjects of geometric probability and integral geometry and the more modern one of stochastic geometry in rather a novel way to provide a unifying framework in which they can be studied. The author focuses on factorisation properties of measures and probabilities implied by the assumption of their invariance with respect to a group in order to investigate non-trivial factors. The study of these properties is the central theme of the book. Basic facts about integral geometry and random point process theory are developed in a simple geometric way so that the whole approach is suitable for a non-specialist audience. Even in the later chapters where the factorisation principles are applied to geometrical processes the prerequisites are only standard courses on probability and analysis. The main ideas presented here have application to such areas as stereology and tomography geometrical statistics pattern and texture analysis. This book will be well suited as a starting point for individuals working in those areas to learn about the mathematical framework. It will also prove valuable as an introduction to geometric probability theory and integral geometry based on modern ideas. Language: English