An introduction to mirror manifolds ; A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory ; Topological mirrors and quantum rings ; Mirror manifolds and topological field theory ; Rational curves and classification of algebraic varieties ; Rational curves on Calabi-Yau threefolds ; Picard-Fuchs equations and mirror maps for hypersurfaces ; Kahler classes on Calabi-Yau threefolds -- An informal survey ; Automorphic functions and special Kahler geometry ; Picard-Fuchs equations and flat holomorphic connections from = 2 supergravity ; A new geometry from superstring theory ; The geometry of Calabi-Yau orbifolds ; Properties of superstring vacua from (topological) Landau-Ginzburg models ; An L(2,\mathbb {C}) action on certain Jacobian rings and the mirror map ; A generalized construction of mirror manifolds ; New constructions of mirror manifolds: Probing moduli space far from Fermat points ; Deformations of Calabi-Yau Kleinfolds ; Smoothing 3-folds with trivial canonical bundle and ordinary double points ; Modified Calabi-Yau manifolds with torsion ; Calabi-Yau threefolds and complex multiplication