  We survey a very general (nonlinear) Fredholm theory for a new class of
ambient spaces, called polyfolds. This theory is being currently developed
jointly with K. Wysocki and E. Zehnder. The basic feature of these new spaces
is that in general they may have locally varying dimensions. These new spaces
are needed for a functional analytic treatment of nonlinear problems involving
analytic limiting behavior. This theory is applicable to Gromov-Witten and
Floer Theory as well as Symplectic Field Theory.
