The goal of this school is to introduce the students to basic questions and methods in dynamical systems through concrete examples. Our basic questions are: Existence of cloded orbits, integrability (ie, complete solvability), and stability. And the methods are: geometrization and variational principles. We shall do this by illustrating these questions and methods by elementary and archetypical examples of dynamical systems: Billiards, geodesic and magnetic flows, and the 3-body problem.
Another goal is to show that these basic examples and the question we ask are by no means dry mathematical abstractions, but have their origin in concrete problems such as mechanics, geometrical optics, and celestial mechanics.