In mathematics, plane geometry refers generally to geometry in a two-dimensional space called a plane.
- Euclidean plane geometry, is the most common meaning; it includes
- Plane analytic geometry
- Plane synthetic geometry
- Plane projective geometry, the geometry of projective planes
- Geometry of finite planes, such as the Fano plane
- Affine geometry of affine planes
- Geometry of non-Euclidean planes, including
- hyperbolic planes,
- elliptic planes
- two-dimensional spherical geometry.