Convexity and geometric probabilities

In the development of the subject of Geometric Probabilities, there was always a close relationship to Convex Geometry. In these lectures, I want to demonstrate this relationship with a number of examples. These examples are of different types, since I want to cover various aspects. I start with hitting probabilities for convex bodies, which can be treated by means of integral geometry. Then I want to explain how several classical results on convex bodies can be applied to solve some extremal and uniqueness questions for various parameters connected with random systems of convex sets. The third topic will be more elementary in view of the questions to be asked, but not so as far as some of the answers are concerned: I will consider convex hulls of finitely many random points, under various different aspects.