The book "Stochastic and Integral Geometry" provides a comprehensive introduction to the concepts of stochastic geometry and integral geometry. It is aimed at mathematically oriented readers and covers the fundamental stationary models used in stochastic geometry, such as random sets, point processes, and random mosaics. The development of these disciplines is closely linked to real-world applications in various sciences that require solid mathematical foundations. The book also explores geometric means in relation to invariant measures, making it a suitable tool for analyzing random geometric structures that are invariant under translations or movements. Additionally, it presents fundamental results from the interplay of both disciplines and includes a chapter on selected problems of geometric probabilities, as well as a look ahead to non-stationary models.