The course of axiomatic geometry is beyond my knowledge of math. However, I was wondering why there is no forum for this subject on this site.
Are you talking about the stuff they teach in pre-calculus?
In university there are many different kinds of geometry (and it can get very very complicated). Differential geometry is the form of geometry that is more general than the n-dimension stuff they cover in under-graduate university courses and it is taught often in final year undergraduate or in graduate school. In order to do this, you will probably need to do a math degree with enough honors courses.
If its high school though, the Basic Mathematics book should cover it (I think).