In physics, mathematical quantization applies abstract mathematical formulations to describe the process of quantizing classical Hamiltonian and Lagrangian systems, and in particular, quantizing line bundles that are defined on symplectic manifolds. Mathematical quantization uses the modern mathematics techniques of differential geometry to accomplish this task.

A different but related approach to quantization in noncommutative mathematics, which is not based on Hamiltonian mechanics, is seen through the quantization of algebraic groups, such as by Hopf algebras, the Virasoro algebra and the Kac–Moody algebra. The result of quantization leads to the study of noncommutative geometry whereby Connes emphasized C*-algebras.

A version of quantization for functions is q-analogs.