  We 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.
