Introduction: Hamiltonian flows, the Arnold and Weinstein conjectures, examples: convex Hamiltonians and flows on twisted cotangent bundles, review of results.

Floer homology: review of Morse theory, Floer homology and symplectic homology, application: the Arnold conjecture.

Almost existence theorems for periodic orbits: symplectic capacities almost existence and the Hofer-Zehnder capacity, application: Viterbo's proof of Weinstein conjecture and almost existence in twisted cotangent bundles.

The Hamiltonian Seifert conjecture: the Seifert conjecture and counterexamples, Hamiltonian dynamical systems without periodic orbits.