Functional integration is a collection of results in mathematics and physics where the domain of an integral is no longer an ordinary region of space, but a space of functions. Functional integrals appear in probability, in the study of partial differential equations, and in the path integral formulation to the quantum mechanics of particles and fields. While the term suggests an extension of ordinary integration, the lack of a translation-invariant measure on infinite-dimensional spaces means that functional integrals must be defined by more subtle methods or interpreted formally.