[hugh]

If you want to go to the fundamentals, I'd suggest The Principles of Mathematics by Bertrand Russell. It won't tell you much about the specific sub-branches of mathematics, but it's a good introduction to mathematics the way mathematicians see it, as opposed to mathematics the way high-school students (or teachers, for that matter) see it.

To give you an idea of the flavour of it, here's the opening sentence:

"Pure Mathematics is the class of all propositions of the form p implies q, where p and q are propositions containing one or more variables, the same in the two propositions, and neither p nor q contains any constants except logical constants."

It's way out of copyright, so there's an online version:

http://fair-use.org/bertrand-russell/the-principles-of-mathe...