The newly estabilished Centro di Ricerca Matematica “Ennio De Giorgi” began its activities hosting a Research Trimester on Dynamical Systems, from February 4th through April 26th, 2002. In the two volumes some of the contributions have been collected. The contributions are in the following different fields: Holomorphic dynamics and foliations, Hamiltonian dynamics, Small divisor problems, Celestial mechanics, Ergodic theory and randomly perturbed systems, Periodic orbits and zeta functions, Topology and dynamics, Partially hyperbolic and non-uniformly hyperbolic systems, Bifurcation theory and related topics, Dynamics on non archimedean fields.