Geometry has three basic types or "kinds" in terms of mathematics. An easier way to describe the difference between these three types is to compare each geometrys definition of a triangle.
These three types are:
- Hyperbolic Geometry - In which the sum totals of angles of a triangle must add up to less than 180 degrees this is non-Euclidian as it's not viewed in a flat space.
- Euclidian Geometry - Traditional geometry which is viewed on a infinite flat plane in 2D. The principle here is that triangles should have 3 angles which equate to a total of 180 degrees.
- Elliptic Geometry - In Elliptic Geometry triangles should have three angles which total higher than 180 degrees.
Geometry in Maths
Now I can't profess to be anything of a maths genius but I did find this video which gives a good grounding in the basic principles of geometry!