These lecture notes contain the main topics presented in a series of lectures given at the Scuola Normale di Pisa in the academic years 1998-1999-2000. The audience was made up of students of the last two years of the Physics program and a few Ph.D. students. The lectures address selected topics in stellar dynamics, presented in a deductive approach. Completeness is by no means the final goal of this work. The course is divided into two parts. In the first part, basic mathematical concepts are introduced, with some discussion of their physical meaning. In the second part, the tools developed are applied to an extensive discussion of selected problems offered by the stellar dynamics of collisionless systems of stars.