The aim of the meeting is to summarize and critically asses the collective researches of the PRIN group "Dynamical Systems and Applications" (PRIN 2007B3RBEY) in the field of dynamical systems both for finite and infinite number of degrees of freedom. It also aims at discussing further lines of development for the research in the areas for Celestial Mechanics, statistical properties of Dynamical Systems, Hamiltonian PDE, Fermi-Pasta-Ulam lattices and other infinite dimensional models related to transport problems in non-equilibrium Statistical Mechanics.