There are roughly the following parts: 1, analysis: including mathematical analysis, real variable function, functional analysis, complex analysis, harmonic analysis, Fourier analysis, ordinary differential equations, partial differential equations and so on. 2. Number theory: including elementary number theory, algebraic number theory, analytic number theory, number geometry, Diophantine approximation theory, module form, etc. 3. Algebra: elementary algebra, advanced algebra, modern (or abstract) algebra, commutative algebra, homology algebra, Lie algebra, etc. 4. Geometry: elementary geometry, advanced geometry, analytic geometry, differential geometry, Riemannian geometry, tensor analysis, topology, etc. 5. Applied mathematics: There are too many branches, such as probability statistics, numerical analysis, operational research, queuing theory and so on.