I'm looking for a good introductory text to analysis, or, more specifically, a text that puts calculus on a much more rigorous ground. I've just finished a year of calculus at my local university, and I feel a bit cheated by the course I took. In addition to having a poor teacher who focused on rote memorization, our text was abysmal. I ended up resorting to self study, which was a blessing in disguise because it led me to discover a love of logic, set theory, abstract algebra, and topology.
I'm interested in becoming a math major when I graduate hs, and I'm comfortable with studying dense, more sophisticated texts as long as they are well written, comprehensive, and build the subject on the ground up. Online texts would be appreciated, as I'm spending the next few months travelling and wont be able to receive packages.