Title: Lectures on symplectic topology

Abstract: The goal of these lectures is to provide an introduction to symplectic topology, by way of the theory of symplectic capacities, which are symplectic invariants of symplectic manifolds, and which have been used to settle numerous long-standing conjectures (existence of periodic orbits of Hamiltonian systems, the Weinstein conjecture, etc.). We will provide an axiomatic definition of symplectic capacities and construct one such capacity (the Hofer-Zehnder capacity), with applications to the study of symplectic diffeomorphisms and symplectic embeddings. Time-permitting, Floer's approach to Morse theory will also be presented.