Isomorphism is a very general concept that appears in several areas of mathematics. The word derives from the Greek *iso*, meaning "equal," and *morphosis*,
meaning "to form" or "to shape."

Formally, an isomorphism is bijective morphism. Informally, an isomorphism is a map that preserves sets and relations among elements. " is isomorphic to " is written . Unfortunately, this symbol is also used to denote geometric congruence.

An isomorphism from a set of elements onto itself is called an automorphism.