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Focusing on convex geometry in Euclidean space, this book introduces fundamental concepts and results, progressing to the Brunn-Minkowski theory, including mixed volumes and the Brunn-Minkowski inequality. It also explores key topics like surface area measures, projection functions, zonoids, and geometric valuations. An introduction to integral-geometric formulas concludes the text. The inclusion of numerous exercises and supplementary materials enhances the learning experience, making it a comprehensive resource for students and researchers alike.

Stochastic geometry deals with models for random geometric structures. Its early beginnings are found in playful geometric probability questions, and it has vigorously developed during recent decades, when an increasing number of real-world applications in various sciences required solid mathematical foundations. Integral geometry studies geometric mean values with respect to invariant measures and is, therefore, the appropriate tool for the investigation of random geometric structures that exhibit invariance under translations or motions. Stochastic and Integral Geometry provides the mathematically oriented reader with a rigorous and detailed introduction to the basic stationary models used in stochastic geometry – random sets, point processes, random mosaics – and to the integral geometry that is needed for their investigation. The interplay between both disciplines is demonstrated by various fundamental results. A chapter on selected problems about geometric probabilities and an outlook to non-stationary models are included, and much additional information is given in the section notes.