ABSTRACT
This is an expository account of some topics on Hamiltonian systems which were presented in four lectures held at Purdue University. It was our intention to discuss questions like stability, existence of integrals, and existence of quasi-periodic solutions, all problems which have been of interest for a long time but where there has been definite progress within the last ten years, due to the work of Kolmogorov, Arnold and others. Those basic problems mentioned above appear in various forms in the theory but in greatest simplicity if one studies Hamiltonian systems near an equilibrium solution. For this reason we restrict ourselves to a large extent to this situation.
