Introduction to symplectic field theory

We sketch in this article a new theory, which rye call Symplectic Field The ory or SFT, which provides an approach to Gromov-Witten invariants of sympl ectic manifolds and their Lagrangian submanifolds in the spirit of topologi cal field theory, and at the same time serves as a rich source of new invar iants of contact manifolds and their Legendrian submanifolds. Moreover, we hope that the applications of SFT go far beyond this framework.(1)