In mathematics, an **isometry** (from the Greek ἴσος, isos, which means equal | called also **congruence**, or **congruent transformation**) is a notion that generalizes that of rigid movement of an object or a geometric figure. Formally, it is a function between two metric spaces that preserves distances.

Examples of isometries are translations, rotations, and reflections in the plane or space. Generally, isometries retain, in addition to distances, other geometric concepts such as angles, areas, and lengths.