Mathematically, the topology (number of holes) of any object in our daily life (chairs, tables, cups...) is given by the integration of the Gaussian curvature of its surface. In a similar manner, the integration of a certain curvature calculated from the quantum mechanical wave function of a solid determines the topology of the solid. I will demonstrate that at the topological phase transitions (when number of holes changes), the curvature generally diverges at certain momentum. Through this divergence, a number of aspects we are familiar with in statistical mechanics can be introduced into topological phase transitions, including correlation function, critical exponents, scaling laws, universality class, and renormalization group. This approach points to a unified picture for the topological phase transitions in any known solids, regardless the dimensionality or symmetry class, and with or without many-body interactions.