Supersymmetric Yang-Mills Theory

We present a series of four self-contained lectures on the following topics; (I) An introduction to 4-dimensional 1 ≤ N ≤ 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.