Global aspects of periodic solutions of nonlinear conservative system -- Lecture 1: On resonant hamiltonian systems with finitely many degrees of freedom. -- Lecture 2: Realizations of the reduced phase space of a hamiltonian system with symmetry -- KAM Today -- Note on the evolution of the Lie-Deprit transform -- Lie transforms: A perspective -- The covariant lie-transformed plasma action principle -- Geometric Hamiltonian structures and perturbation theory -- Lie point transformation group solutions of the nonlinear Vlasov-Maxwell equations -- A constructive solution to the Hamilton-Jacobi equation -- Local and global aspects of a generalized Hamiltonian theory -- Particle channeling in crystals and the method of averaging -- Rigorous stability results on crystal channeling via canonical maps -- Some considerations for a theory of approximate invariants -- Exact invariants in the form of momentum resonances for particle motion in one-dimensional, time-dependent potentials.