Definition:Affine Geometry

Definition
Affine geometry is the study of the geometry of affine spaces.

Hence it is the study of properties and types of geometric figures which are invariant under an affine transformation.

It provides a modern axiomatic approach to the study of configurations of lines, planes and hypersurfaces.

In particular an affine space can be thought of as a finite dimensional vector space with no distinguished origin, and its affine transformations are those that preserve collinearity.