Quasi integrable mechanical systems

This is a review paper on classical perturbation theory for nearly-integrable Hamiltonian systems. The subjects covered by the paper are the following: the Arnold-Liouville theorem; the Birkhoff series; an application to the study of the precession of Mercury's perihelion, due to Jupiter's disturbance; the Nekhoroshev theorem, including the case of weakly coupled harmonic oscillators (a new result), and also, for the nonisochronous case, an important application to the study of the local chaotic motions inside resonances (another new result); finally, the KAM theorem.