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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Homological mirror symmetry is a mathematical conjecture made by Maxim Kontsevich. It seeks a systematic mathematical explanation for a phenomenon called mirror symmetry first observed by physicists studying string theory. In an address to the 1994 International Congress of Mathematicians in Zurich, Kontsevich speculated that mirror symmetry for a pair of Calabi-Yau manifolds X and Y could be explained as an equivalence of a triangulated category constructed from the algebraic geometry of X and another triangulated category constructed from the symplectic geometry of Y.