2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149961We review the applications of mirror symmetry to the study of the moduli spaces of two-dimensional conformal field theories with $N{=}(2,2)$ supersymmetry, particularly those constructed from Calabi--Yau manifolds. (Lecture delivered at the Zurich ICM, section on mathematical physics.)11 pages, AmS-TeX v2.1, no figures, author-supplied dvi file at ftp://ftp.math.duke.edu/preprints/94-06.dviAlgebraic Geometrytext