I'm looking for math books that leave you understanding why things work, not just how to do them. Any level counts, from elementary arithmetic through undergraduate math.
By "conceptually" I mean you come away understanding why the rules and methods are true. How the book gets you there doesn't matter: clear explanations, pictures, well-ordered problems, worked examples, or proofs.
Any kind of book counts: textbooks, short books on one topic, problem books, books written for teachers, popular books, old or out-of-print books, and good translations. Any subject counts too: arithmetic, algebra, geometry, trigonometry, calculus, linear algebra, probability, differential equations, and so on.
If you recommend a book, it would really help to include:
Title and author (and the edition, if it matters)
One or more things it made you understand, and how it did that.
Whether you studied it on your own or in a class.
Thanks!