"The past few years have seen several exciting developments in the field of symplectic geometry, and a beginning has been made towards solving many important and hitherto inaccessible problems. The new techniques which have made this possible have come both from the calculus of variations and from the theory of elliptic partial differential operators. This paper describes some of the results that obtained using elliptic methods, and then shows how applied these elliptic techniques to develop a new approach to , which has important applications in the theory of 3- and 4-manifolds as well as in symplectic geometry."