Symplectic manifolds and Hamiltonian dynamical systems

This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete integrability of these systems, with detailed proofs. Several explicit calculations for which references are not immediately available are given. These results are exemplified by applications to some Hamiltonian dynamical systems.