This is the second and considerably extended edition of the book of the same authors published in 1987. The applied style of presentation has not changed. But important developments on topics like Boolean models, stereology, random tesselations, Gibbs processes and random shapes have been added. The book covers a large variety of ideas and models which are used in stochastic geometry and also gives an introduction to the statistical analysis of these models. Applications of these models are numerous in several fields e.g. in geology, material sciences, biological models of tissues, agriculture, landsat data. The origin of this field is to find in the problem to recover information on threedimensional structures when only information on one-or two-dimensional sections is available.From this origin a rich field of science has emerged. The book describes underlying general concepts like point processes, random sets and random measures and gives an introduction to the most prominent special models like Poison processes, hard-core and Gibbs-processes, the Boolean-model, fibre and surface processes and the Voronoitesselation.The main aim of the book is to make these developments available to the applied scientist and at the same time to give a mathematical exact exposition including the recent and relevant research.As consequence of this concept the level of exposition is uneven. In some parts the explanations are heuristic or by examples and often without detailed mathematical proofs. But the reader gets a unique introduction and perspective of the potential use of the models and the underlying basic mathematical concepts. In its kind there is no equally informative and readable exposition. L. R~SCHENDORF

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