GEOMETRY OF N = 2 STRINGS

We study various aspects of N = 2 critical strings. The most important aspect of these theories is that they provide a consistent quantum theory of self-dual gravity in four dimensions. We discuss the geometrical aspects of the vacua and their relation to twistor space, W-infinity, harmonic superspace and the superstring world-sheet. We find many indications that suggest that many of the results valid for physics in two dimensions have analogs in the effective four-dimensional theory of N = 2 strings.