Introduction:

Recently there have been significant mathematical breakthroughs in Celestial Mechanics, concerning difficult problems: always more precise information about the linear stability and instability of some relative equilibrium configurations as well as of some collisionless periodic solutions, discovery of new quasiperiodic or periodic orbits with new kinds of symmetries, new results on nonintegrability, sharper results from averaging methods and KAM theory. The purpose of this special session is to bring the main specialists in the Nbody problem together with the leaders of different areas in dynamical systems (Variational Methods, Mather Theory, Hamiltonian dynamics, Ergodic Theory) trying to build a theoretical framework suitable to attack some of the many unsolved aspects of the Nbody problem. 
