The class aims to discuss progress in higher dimensional geometry. The central theme is the classification theory of varieties. It covers recent results in fields including minimal model program, moduli of varieties, K-stability theory of Fano varieties, boundedness of varieties, explicit geometry of special varieties etc. Students are required to have a solid footing on algebraic geometry, e.g. materials in Hartshorne's book; and are recommended to have basic knowledge of the minimal model program, e.g. Kollár-Mori's book.