Euclidean geometry where the Parallel postulate is modified. It corresponds to Riemannian manifolds with non-zero Curvature

Elliptic geometry

Hyperbolic geometry

Riemannian geomtry

Differential geometry

See pages 88 and forth in GEB

https://www.youtube.com/watch?v=IwDY0JmXUc4

https://twitter.com/ZenoRogue