Mathematical geology is a new and important branch of geological sciences. This paper deals with the main advances of mathematical geology in the following fields; applications of fractal, dissipative structure, grey system models and fuzzy mathematics in geology. Fractal has been used successfully in the study of impalpable structure of metacrystals, fault systems and geological structure distribution, porous medium, surface roughness of geological bodies and other problems. Dissipative structure has been applied in the study of dissociation of minerals, dynamics of hydrothermal mineralization, genesis of migmatite, structure and motions of the earth' s crust and mantle and so on. Grey system models have been used in many problems of hydrogeology, engineering geology, environmental geology and mineral deposit predictions. Fuzzy mathematics is a widely usd quantitative tool for solving many geological problems. Finally, trends of development of mathematical geology are discussed.