An Overview on the Nekhoroshev Theorem -- Diffusion in Hamiltonian Quasi-Integrable Systems -- Weakly Dissipative Systems in Celestial Mechanics -- Connectance and Stability of Dynamical Systems -- Chaotic Di?usion of Asteroids -- An Overview of the Rotations of Planets in the Solar System -- On the Stability of Extra-Solar Planetary Systems -- Origin Theories for the Eccentricities of Extrasolar Planets -- Methods for the Study of the Dynamics of the Oort Cloud Comets I: Modelling the Stellar Perturbations -- Methods for the Study of the Dynamics of the Oort Cloud Comets II: Modelling the Galactic Tide -- Special Features of Galactic Dynamics -- On the Diffculty to Foresee Solar Cycles: A Non-Deterministic Approach.

This set of lectures collects surveys of open problems in celestial dynamics and dynamical astronomy applied to solar, extra-solar and galactic systems. Emphasis is on questions of stability of planetary systems. In particular the discovery and thus the possibility to study many new extra-solar planetary systems have spurred new developments in the field and enabled the testing and enlargement of the domains of validity of theoretical predictions through the Nekhoroshev theorem.