This is a review
from my collection of math book reviews
Calculus by Michael Spivak
This is a book everyone should read. If you don't know calculus and have the time, read it and do all the exercises. Parts 1 and 2 are where I finally learned what a limit was, after three years of "explanations" from bad calculus books. The whole thing is the most coherently envisioned and explained treatment of one-variable calculus I've seen; Spivak's plan and the nature of the insight he's trying to impart are evident throughout.
The book has flaws, of course. The exercises get a little monotonous because Spivak has a few tricks he likes to use repeatedly to construct them. There is perhaps too little material on applications, but this can be found in other books (try Apostol's Calculus, or Differential and integral calculus by Courant if you're brave). Also, Spivak sometimes avoids sophistication at the expense of clarity, as in the proofs of Three Hard Theorems in chapter 8 (where a lot of epsilon-pushing takes the place of the words "compact" and "connected"). Nevertheless, this is the best calculus book overall, and I've seen it do a wonderful job of brain rectification on many people.
Addendum from Pete Clark, one of my co-reviewers: Yes, it's good, although perhaps more of the affection comes from more advanced students who flip back through it? Most of my exposure to this book comes from tutoring and grading for 161 [the University of Chicago honors first-year calculus class], but I seriously believe that working as many problems as possible (it must be acknowledged that many of them are difficult for first year students, and a few of them are really hard!) is invaluable for developing the mathematical maturity and epsilonic technique that no math major should be without.