I learn that Geometry has several categories/subfields from Wikipedia. But I am still not clear about the standards according to which they are classified.
It seems Euclidean Geometry, Affine Geometry and Projective Geometry are classified according some rule, while Hyperbolic Geometry, Elliptic Geometry and Riemann Geometry according to another, and Axiomatic, Analytic, Algebraic and Differential Geometry perhaps according to a different one? What rules are they?
Are Affine Geometry, Projective Geometry, Hyperbolic Geometry, Elliptic Geometry and Riemann Geometry all Non-Euclidean Geometry? What are their common characteristics that make them Non-Euclidean Geometry?
Really appreciate if someone could clarify these questions for me and also hope you can provide more insights into the subfields of Geometry not necessarily the specific questions I asked.
Update: Although my major is not math, I have been involved in some projects requiring quite a few mathematics and have taken a lot of courses in mathematics on undergraduate/graduate level. Now looking back, I am confused about what I have learned and heard, and would like to get a big picture.
