Hamiltonian Systems of Few Degrees of Freedom.- Equilibrium Points, Periodic Orbits and Local Stability.- Efficient Indicators of Stable and Chaotic Motion.- FPU Recurrences and the Transition from Weak to Strong Chaos.- Localization and Diffusion in Nonlinear 1-Dimensional Lattices.- The Statistical Mechanics of Quasi-Stationary States.- Conclusion, Open Problems and Future Outlook.