Recent advances in the study of the existence of periodic orbits of Hamiltonian systems -- The direct method in the study of periodic solutions of Hamiltonian systems with prescribed period -- Periodic solutions of Hamiltonian systems having prescribed minimal period -- Duality in non convex variational problems -- La thรฉorie de la seconde variation et le problรจme linรฉaire quadratique -- Mรฉthodes asymptotiques dans lโ{128}{153}รฉtude de systรจmes hamiltoniens non autonomes -- Numerical research of periodic solutions for a Hamiltonian system