Here are two much older books, but worth your consideration.
Creative Mathematics by Herbert Wall.
Mathematical Snapshots by H. Steinhaus
Hey, does anyone recommend any?
I am currently entering my second year of Further Maths pre-uni and I recently bought a book that looked promising called 'The Art and Craft of Problem Solving' by Paul Zeitz.
I'm mainly trying to work on my ability to problem solve. Trying to work out certain proofs etc which I am sure will help for University. In College all we do really is a tiny little work on Proofs and my main problem with learning Maths pre-Uni is you learn to answer everything in a very systematic manner. You never truly "answer" a question you simply remember the process in which you obtain said answer.
Anyway, enough blabbing. Anyone know any good books?
I am going to strongly recommend:
Amazon.com: Introduction to Analysis (9780130811325): Arthur P. Mattuck: Books
I don't know what your background is, but this book is easy enough to follow if you have a bit of calculus.
It is a strangely beautiful treatment of the Reals, and can serve as an introduction to proofs.
edit I noticed the pre-uni thing... This may not be appropriate, then. A really exceptional book, though.
You might take a look at "The Heart of Mathematics":
Amazon.com: The Heart of Mathematics: An Invitation to Effective Thinking (Key Curriculum Press) (9780470424766): Edward B. Burger, Michael Starbird: Books