to FPU.- Dynamics of Oscillator Chains.- Role of Chaos for the Validity of Statistical Mechanics Laws: Diffusion and Conduction.- The Fermi-Pasta-Ulam Problem and the Metastability Perspective.- Resonance, Metastability and Blow up in FPU.- Center Manifold Theory in the Context of Infinite One-Dimensional Lattices.- Numerical Methods and Results in the FPU Problem.- An Integrable Approximation for the Fermi-Pasta-Ulam Lattice.