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In the past few decades many attempts have been made to search for a consistent formulation of quantum field theory beyond perturbation theory. One of the most interesting examples is the Seiberg-Witten ansatz for the N=2 SUSY supersymmetric Yang-Mills gauge theories in four dimensions. The aim of this book is to present in a clear form the main ideas of the relation between the exact solutions to the supersymmetric (SUSY) Yang-Mills theories and integrable systems. This relation is a beautiful example of reformulation of close-to-realistic physical theory in terms widely known in mathematical

Seiberg-Witten invariants. --- Four-manifolds (Topology) --- String models. --- Models, String --- String theory --- Nuclear reactions --- 4-dimensional manifolds (Topology) --- 4-manifolds (Topology) --- Four dimensional manifolds (Topology) --- Manifolds, Four dimensional --- Low-dimensional topology --- Topological manifolds --- Invariants --- Seiberg-Witten invariants --- String models --- Variétés topologiques à 4 dimensions --- Modèles des cordes vibrantes (Physique nucléaire)