In geometry and mathematical analysis, an **isometry** is a distance-preserving mapping. This idea occurs in the theories of metric spaces, normed vector spaces and inner product spaces; also in quadratic forms and differential geometry.

In Euclidean space with the usual distance function, the isometries can be characterized: there are no more than the 'expected' examples generated by rotations, reflections and translations. To put this more accurately, the isometries form a group, that is the semidirect product of the orthogonal group and the group of translations. (This group is sometimes called the Galilean group, at least for three dimensions and in relation with its role in Newtonian mechanics as expressed by permissible changes of frame of reference. See Galilean transformation.)

## Plane isometries; glide reflections

See also: congruence (geometry), similarity (mathematics).

Angle-preserving mappings are called conformal.

Isometric projection or isometric view is the name given to a type of technical drawing / projection used in fields such as Mechanical Engineering or Architecture that makes an object/ building visible from three planes/co-ordinates.