Guided by the viewpoint of transformation group and taking some important theorems as the main line, advanced geometry introduces the basic knowledge of plane projective geometry, trying to show the rich contents and internal relations of projective geometry, affine geometry, Euclid geometry, hyperbolic geometry and elliptic geometry. The contents include: projective plane, projective mapping, projective theory of conic, affine geometry and Euclidean geometry, plane hyperbolic geometry, plane elliptic geometry and so on. Advanced Geometry can be used as a textbook for the department of mathematics in normal universities, and can also be used for self-study.