  We describe a very general (nonlinear) Fredholm theory for a new class of
ambient spaces, called polyfolds. 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.
