Collecting the best books mentioned on hacker news, reddit and other places
I wouldn't recommend Spivak for self-study and a first exposure to analysis. It's known to be notoriously difficult even for good students.
I learned from this Dover book; I think it's pretty good. From there you might move up to Baby Rudin, but it might have a lot of typos, or big gaps in the exposition that are taken to be obvious but require several steps to fill in, since that was certainly the case for Papa Rudin.
: https://www.amazon.com/Introduction-Analysis-Dover-Books-Mat... : https://www.amazon.com/Principles-Mathematical-Analysis-Inte... : https://www.amazon.com/Real-Complex-Analysis-Higher-Mathemat...
I highly recommend this book for Real Analysis http://www.amazon.com/Introduction-Analysis-Maxwell-Rosenlic...
We used it at the University of Texas at Austin for the first semester in Real Analysis. I found it very clear and easy to follow.