Gauge theory, symplectic geometry and symplectic topology are significant areas at the crossroads of several mathematical disciplines. The text includes surveys of recent developments in these areas, such as some of the first expository material of Seiberg-Witten theory. Topics covered include: introductions to Seiberg-Witten theory, to applications of the S-W theory to four-dimensional manifold topology, and to the classification of symplectic manifolds; an introduction to the theory of pseudo-holomorphic curves and to quantum cohomology; algebraically integrable Hamiltonian systems and moduli spaces; the stable topology of gauge theory, Morse-Floer theory; pseudo-convexity and its relations to symplectic geometry; generating functions; Frobenius manifolds and topological quantum field theory.