内容：
Homological mirror symmetry is a relation between algebraic and symplectic sides of a geometric object. Original mirror symmetry came from physics, but homological mirror symmetry conjecture formulated by M.Kontsevich for Calabi-Yau varieties is an attempt to give a mathematical explanation of this phenomenon. We will try to describe main principles of homological mirror symmetry and the extension to a non-Calabi-Yau case.