2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60065We sketch in this article a new theory, which we call Symplectic Field Theory or SFT, which provides an approach to Gromov-Witten invariants of symplectic manifolds and their Lagrangian submanifolds in the spirit of topological field theory, and at the same time serves as a rich source of new invariants of contact manifolds and their Legendrian submanifolds. Moreover, we hope that the applications of SFT go far beyond this framework.102 pages, 4 figuresSymplectic GeometryMathematical PhysicsAlgebraic Geometry53D40, 53D45text