An *n*-dimensional *manifold* is a topological space which is locally Euclidean. That is, every point lies in a region which looks like the space **R**^{n}.

A 1-manifold is a curve, a 2-manifold is a surface, etc.

Manifolds which have a structure which allow differentiation to be performed are called *differentiable manifolds* and if differentiation can take place arbitrarily often they are called *smooth manifolds*.