In mathematics, the affine group or general affine group of any affine space is the group of all invertible affine transformations from the space into itself. In the case of a Euclidean space (where the associated field of scalars is the real numbers), the affine group consists of those functions from the space to itself such that the image of every line is a line.
Over any field, the affine group may be viewed as a matrix group in a natural way. If the associated field of scalars is the real or complex field, then the affine group is a Lie group.