Canonical perturbation theory for nearly integrable systems

These lectures are devoted to the main results of classical perturbation theory. We start by recalling the methods of Hamiltonian dynamics., the problem of small divisors, the series of Lindstedt and the method of normal form. Then we discuss the theorem of Kolmogorov with an application to the Sun-Jupiter-Saturn problem in Celestial Mechanics. Finally we discuss the problem of long-time stability, by discussing the concept of exponential stability as introduced by Moser and Littlewood and fully exploited by Nekhoroshev. The phenomenon of superexponential stability is also recalled.