Through analyzing the invariants in map projection and according to the condi-tions whether there are any directions along which length of segements is true, the author finds that the projections can be mainly divided into three categories, i.e., elliptic, parabolic and hyperbolic. A new way of studying map projection has been derived and the problems remained in Prof. Wu's monograph "mathematic carto-graphy" (1964, in Chinese) are solved.