Without knowing your background, Pugh's and Abbott's are usually good choices as are Schramm's Dover, and while not really analysis texts, don't forget the classic fundamentals/foundations books by Courant/Robbins What is Mathematics, Ian Stewart/D Tall Foundations of Math, Felix Klein etc

Here's lots of reviews: https://www.maa.org/tags/real-analysis

https://math.stackexchange.com/questions/tagged/real-analysi...

https://www.reddit.com/r/math/wiki/faq#wiki_what_are_some_go...

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[1]; I think it's pretty good. From there you might move up to Baby Rudin[2], 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[3].

[1]: https://www.amazon.com/Introduction-Analysis-Dover-Books-Mat... [2]: https://www.amazon.com/Principles-Mathematical-Analysis-Inte... [3]: https://www.amazon.com/Real-Complex-Analysis-Higher-Mathemat...

Calculus, by Spivak (an analysis textbook despite the name). I found this book clear, with good exercises, and it starts at the very beginning. I think the most difficult exercises are in the early chapters, so stick with it!

Try Terence Tao's Analysis I and II.