[jfv]

Do NOT read Rudin. He is terse and unless you are already well versed in mathematics it is simply incomprehensible.

My recommendation would be Spivak’s calculus. There are a million great exercises and the book is beautifully typeset and overall a pleasure to read. Don’t let the title fool you, there are analysis exercises in there.

[x0x0]

You have to decide between two things:

1 - you want to learn to prove things. Then yes, Rudin is a shitty text to learn by yourself because he really likes a certain type of, for lack of a better phrase, "beautiful" proof that requires a bunch of insightful jumps to get to. He'll then show the proof and really not discuss about how he got there. What a student needs is the ability to string facts/theorems that he or she knows together and how to turn that into a proof. Without a good professor, Rudin is (imo) terrible for that.

2 - you want to learn analysis, and care less about proving things. Reasons for this may be you need a bit the underpinnings for various reasons, and you care less about proving things and more about understanding. I think Rudin is a pretty good text then.

Spivak's calculus is a great book but be prepared to spend a lot of hours on it.

[AlexCoventry]

I LOVED Rudin. It was a long time ago, though.

At the very least, it has great exercises.

I also loved Spivak.