  We prove the classical mirror symmetry conjecture for the mirror pairs
constructed by Berglund, H\"ubsch, and Krawitz. Our main tool is a
cohomological LG/CY correspondence which provides a degree-preserving
isomorphism between the cohomology of finite quotients of Calabi-Yau
hypersurfaces inside a weighted projective space and the Fan-Jarvis-Ruan-Witten
state space of the associated Landau-Ginzburg singularity theory.
