Thank you for great replies.
I'm satisfied with the answers to my first question (thank you Pete, KConrad and Charles) and I want to clarify a little bit the second one:
KConrad, there is a course at Harvard - 130. Classical Geometries and at Berkeley Math 130 The Classical Geometries , but these courses are not often recommended for math majors, for example at Harvard "Mathematics 113, 114, 122, 123, 131, and 132 form the core of the departments more advanced courses" - 130 is not even mentioned. MIT, for example, doesn't have a similar course at all. And most of the internet math discussions for undergraduates are concerned with Algebra, Real Analysis and sometimes Topology, and geometry isn't mentioned at all. So I guess either topics like non-Euclidian and projective geometries are integrated into those three major subjects or are considered obsolete for a modern mathematician?
As a recent high school graduate that seems rather odd, because we spent most of the time studying it. Maybe part of my confusion is explained by this discrepancy between high school math and college math. Also, thanks for pointing to UIM, a am planning to enroll the next september.