PrefaceNotationCh. 1Introduction1Ch. 2The Quintic Threefold15Ch. 3Toric Geometry31Ch. 4Mirror Symmetry Constructions53Ch. 5Hodge Theory and Yukawa Couplings73Ch. 6Moduli Spaces113Ch. 7Gromov-Witten Invariants167Ch. 8Quantum Cohomology217Ch. 9Localization275Ch. 10Quantum Differential Equations301Ch. 11The Mirror Theorem331Ch. 12Conclusion397App. ASingular Varieties407App. BPhysical Theories411Bibliography437Index453