  We present a series of four self-contained lectures on the following topics:
  (I) An introduction to 4-dimensional 1\leq N \leq 4 supersymmetric Yang-Mills
theory, including particle and field contents, N=1 and N=2 superfield methods
and the construction of general invariant Lagrangians;
  (II) A review of holomorphicity and duality in N=2 super-Yang-Mills, of
Seiberg-Witten theory and its formulation in terms of Riemann surfaces;
  (III) An introduction to mechanical Hamiltonian integrable systems, such as
the Toda and Calogero-Moser systems associated with general Lie algebras; a
review of the recently constructed Lax pairs with spectral parameter for
twisted and untwisted elliptic Calogero-Moser systems;
  (IV) A review of recent solutions of the Seiberg-Witten theory for general
gauge algebra and adjoint hypermultiplet content in terms of the elliptic
Calogero-Moser integrable systems.
