Summary:  Gauge theory, symplectic geometry and symplectic topology are important areas at the crossroads of several mathematical disciplines. The present book, with expertly written surveys of recent developments in these areas, includes some of the first expository material of SeibergWitten theory, which has revolutionised the subjects since its introduction in late 1994. Topics covered include: introductions to SeibergWitten theory, to applications of the SW theory to fourdimensional manifold topology, and to the classification of symplectic manifolds; an introduction to the theory of pseudoholomorphic curves and to quantum cohomology; algebraically integrable Hamiltonian systems and moduli spaces; the stable topology of gauge theory, MorseFloer theory; pseudoconvexity and its relations to symplectic geometry; generating functions; Frobenius manifolds and topological quantum field theory
