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)).