What books should I get to self study beyond Calculus for someone about to start undergrad mathematics?

I am struggling to pick out books when it comes to self studying math beyond Calculus.

My situation is as follows. I have taken all math courses at my school (up to Calc BC and AP Stats) and I have scored 5's on all of the exams. I am going to major in math at college next year but I really do enjoy learning in my free time and I am out of material. I have looked at some of the stuff on KhanAcademy, but the videos go really slowly and lack depth, so I would prefer something to read.

The only semi math book I have read for fun was Gödel, Escher, Bach which I greatly enjoyed. I am looking for anything, even if it reads similar to a textbook, that could further advance my mathematical knowledge in any way. Thank you.

EDIT 1: All answers do answer my question to some extent, so I will not be accepting an answer but rather using them all. Please continue to answer this question as I enjoy having more material to read.

Don't read anything too advanced, i.e. you should be able to understand everything, so you don't waste your time.

How to Prove It: A Structured Approach - Velleman

Numbers and Geometry - Stillwell

Calculus - Spivak

Linear Algebra Done Right - Axler

I'd recommend (elementary) number theory - save linear algebra for college.

Dover offers many inexpensive titles; you could buy several and read about the same topics from different points of view.

I particularly like Friedberg's offbeat Adventurers Guide to Number Theory. If you visit that book's page http://store.doverpublications.com/0486281337.html then Dover will show you other elementary number theory titles.

Two books turned me on to mathematics when I was in high school, and have been with me as a part of my professional life for years. The first, which I think I saw as a freshman, is Hugo Steinhaus's Mathematical Snapshots, reissued by Dover (http://store.doverpublications.com/0486409147.html). The second was senior year reading: Polya's Induction and Analogy in Mathematics. Free ebook (https://archive.org/details/Induction_And_Analogy_In_Mathematics_1_), paperback Princeton University Press from the MAA (http://www.maa.org/press/maa-reviews/mathematics-and-plausible-reasoning-volume-1-induction-and-analogy), hardbound 1954 edition from alibris (http://www.alibris.com/Mathematics-and-Plausible-Reasoning-Volume-1-Induction-and-Analogy-in-Mathematics-George-Polya/book/28098720?matches=22).

All the books are also available on Amazon, where you will find reviews.

I've been putting together a (large) list of math book recommendations on my blog. (You could start with the basics if you're interested). Two books I would really recommend requiring only calculus that haven't been mentioned yet are

• generatingfunctionology by Herbert Wilf, and

• Concrete Mathematics by Graham, Knuth and Patashnik.

I think the first three chapters (out of 5) of Wilf are very accessible. The fourth using some complex analysis, but I don't recall it being too difficult. Concrete Mathematics is more challenging, but completely awesome. Both books contains exercise solutions in the back.

If you wanted something that was just easy reading I thought

• Symmetry and the Monster by Ronan

about the classification theorem for finite simple groups was a nice "pop" math book and can be read in less than a week.