This book contains the notes of five short courses delivered at the Centro Internazionale Matematico Estivo session Integral Geometry, Radon Transforms and Complex Analysis held in Venice (Italy) in June 1996: three of them deal with various aspects of integral geometry, with a common emphasis on several kinds of Radon transforms, their properties and applications, the other two share a stress on CR manifolds and related problems. All lectures are accessible to a wide audience, and provide self-contained introductions and short surveys on the subjects, as well as detailed expositions of selected results.