Analysis Textbook Does anyone have an recommendations for an Analysis textbook for beginners? I'm looking for a textbook that's like Calculus Third Edition by Smith and Minton in that it's hardcover, has good illustrations and is easy to understand, but I don't want anything that skimps on the proofs.
Thanks
 A: For self-study one could do a lot worse than to begin with Edward D. Gaughan’s Introduction to Analysis before moving on to something more advanced: roughly speaking, it goes back and does the basic theory of the topics typically covered in freshman calculus of one variable. It was designed to be transitional between calculus and graduate-level real analysis, and I remember it as being both rigorous and quite gentle; we used it in a transitional course between calculus and a much harder and more general undergraduate real analysis course.
I liked to use the second edition of Robert G. Bartle’s Elements of Real Analysis when I taught the more advanced real analysis course; it’s especially good on the topological aspects of analysis in $\Bbb R^n$, and on the whole it’s very clearly written.
A: Understanding Analysis by Stephen Abbott.  
Elements of Real Analysis by Charles Denlinger
A: Real Mathematical Analysis by Charles C. Pugh
Elementary Analysis: The Theory of Calculus by Kenneth A. Ross
A: In my (elementary) real analysis class we used a book by Stephen Lay called Analysis With an Introduction to Proof. The reviews are generally positive and I thought it was a great book. My only gripe is that there are no solutions to even/odd numbered exercises except for one or two hints for each section. Also, it's incredibly expensive considering it is about the size of an iPad. In terms of content, it was excellent. There were many examples presented and the proofs were straightforward and easy to comprehend. The text started by covering logic and proof techniques, and even provided some "fill in the blank" proof questions that really eased you into it. I would recommend it for a first text in analysis.
A: Since you have not accepted an answer - and they are all good - I will suggest my favorite.
These are free notes (they almost read verbatim) of a RA course given by Vaughan Jones (Fields Medal winner - aka Nobel for math). They are complete and offer his own treatment, which is indubitably excellent:
https://drive.google.com/viewerng/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxtYXRoMTA0c3AyMDExfGd4OjJiNTJkM2M2ZWUzZGIwYWQ
