Great maths books to read?

If you haven't encountered calculus, get K A Stroud's "Engineering Mathematics". If you've encountered calculus, get K A Stroud's "Advanced Engineering Mathematics". Even if you don't want to be an engineer, it tells you about some really interesting concepts.

Cheers thanks a lot everyone. I think I will get Fermats Last Theorum, A Mathematicians Apology, The Pleasures of Counting, Riemanns Zeros, Engineering Mathematics and God Created the Integers. They should keep me going for a while!

what you should read is Bertrand Russell's Principles of Mathmatics..... amazing book, showing why maths is in everything. a short but masterful work

He said he's an A-level student. I don't see how "Advanced Engineering Mathematics" would be in anyway appropriate for him. Also I don't think the OP had uni level text books in mind....

OP my recommendations:

-"What is Mathematics?" by Richard Courant
-"Language of Mathematics" by Keith Devlin

Both of these should be accessible to someone at your level but have more meat on them than, say, Bill Bryson or Simon Singh (nothing against those authors, just offering a different perspective).

Oh and "Alex's Adventures in Numberland" by Alex Bellos is a bit pop-sciency, but it does offer an interesting fresh take on the "mathematics for idiots" genre.