  Aspects of duality and mirror symmetry in string theory are discussed. We
emphasize, through examples, the importance of loop spaces for a deeper
understanding of the geometrical origin of dualities in string theory. Moreover
we show that mirror symmetry can be reformulated in very simple terms as the
statement of equivalence of two classes of topological theories: Topological
sigma models and topological Landau-Ginzburg models. Some suggestions are made
for generalization of the notion of mirror symmetry.
