LECTURES ON QUANTUM GEOMETRY

In these lectures we discuss the way in which N = 2 superconformal fie ld theory, in the context of string theory, gives rise to geometrical models of spacetime whose quantitative and qualitative properties diff er significantly from their classical (General Relativistic) counterpa rts. After an overview of some general consequences of N = 2 superconf ormal symmetry, we specialize to concrete field theoretic representati ons of this algebra. We indicate how a number of familiar constructs f rom classical geometry naturally arise in these theories, but in a mod ified form giving rise to what is called ''stringy'' or ''quantum'' ge ometry. Our main focus is on mirror symmetry and spacetime topology ch ange.