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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.

Hamiltonian systems. --- Gravitation. --- Astrophysics. --- Systèmes hamiltoniens --- Gravitation --- Astrophysique --- Celestial mechanics --- Extrasolar planets --- Theoretical Astronomy --- Astronomy - General --- Astronomy & Astrophysics --- Physical Sciences & Mathematics --- Solar system --- Physics. --- Dynamics. --- Ergodic theory. --- Observations, Astronomical. --- Astronomy --- Space sciences. --- Astronomy, Observations and Techniques. --- Dynamical Systems and Ergodic Theory. --- Mathematical Methods in Physics. --- Extraterrestrial Physics, Space Sciences. --- Observations. --- Milky Way --- Differentiable dynamical systems. --- Mathematical physics. --- Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics). --- Astronomical physics --- Cosmic physics --- Physics --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Physical mathematics --- Mathematics --- Astronomy—Observations. --- Science and space --- Space research --- Cosmology --- Science --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Astronomical observations --- Observations, Astronomical