An axiomatic foundation of a geometry and the definition of geometry by Klein. Subgeometry of a geometry. Invariants of geometry. Isomorphic geometries. Affine Geometry of ℝⁿ. Euclidean Geometry of ℝⁿ. Spherical Geometry. Mobius Transformations and Reverse Geometry. Projective Geometry. Models of Hyperbolic Geometry. Geometry hierarchy. Connection of Euclidean and non-Euclidean geometries through Projective Geometry.