In mathematics, a **surface** is a generalization of a plane, which is not necessarily flat – that is, the curvature is not necessarily zero. This is analogous to a curve generalizing a straight line. There are many more precise definitions, depending on the context and the mathematical tools that are used to analyze the surface.

The mathematical concept of a surface is an idealization of what is meant by *surface* in science, computer graphics, and common language.

The homeomorphism classes of surfaces have been completely described (see Surface (topology)).