Selecting the Real Analysis Textbooks I am a sophomore in the US with double majors in mathematics and microbiology. I am interested in self-studying real analysis since it will help me with my current research in computational microbiology, prepare for upcoming math research (starting this Fall) on analytic number theory, and prepare for the real analysis course I will take this Fall and Putnam competition.
I just finished Calculus with Analytic Geometry by G. Simmons, How to Prove It by Daniel Velleman, and How to Solve It by G. Polya. I also read some portions of Apostol's Calculus Vol. I to get a deeper view on calculus theories. (I was originally planning to read Apostol's Calculus Vol. I and Spivak's Calculus first, but I think it would be a better idea to start with real analysis since it covers all the ideas in those "advanced calculus" textbooks and much more.)
My current plan is to start with one "dumbed-down" real analysis textbook and one "comprehensive, detailed, and intermediate" textbook, and advance into Rudin's Principles of Mathematical Analysis (required textbook for my real analysis course) starting this Summer, and use it in accordance with other real analysis textbooks. Could you help me on selecting one book from each category?
Elementary Real Analysis textbooks:

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*Elementary Analysis: The Theory of Calculus (Kenneth Ross)

*Understanding Analysis (Steven Abbott)

*The Way of Analysis (Robert Strichartz)

*Real Mathematical Analysis (Charles Pugh)

Intermediate, detailed Real Analysis textbooks:

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*Mathematical Analysis (Tom Apostol)

*Undergraduate Analysis (Serge Lang)

*Introduction to Real Analysis (Bartle, Sherbert)

*Elements of Real Analysis (Bartle, Sherbert)

*Mathematical Analysis I (Vladimir Zorich)

 A: Other than Rudin's analysis text (the first one), I've read Robert Strichartz's "Way of Analysis". Strichartz gives you a lot of motivation and information for most of the concepts, while Rudin just gives you enough for you to do on your own. I favor Rudin's text much more, since I enjoyed the effort required to fill in the gaps and thereby making you "do" a lot during the reading. Additionally, Rudin has a style that I believe many enjoys, for most of his proofs are elegant and stylish. Strichartz will explain much more during, before, and after a proof, but sometimes I feel that his explanations becomes a bit too wordy and too cloudy over the main point. Take it this way: Would you rather try to find a dull sapphire in a messy hay sac, or find a beautiful diamond hiding in a small pile of needles? (one requires sheer effort for something "okay", while the other requires much more effort and care, but to obtain something rather nice.)
I realize that you want to read a more friendly analysis text before Rudin's, but have you considered reading Rudin's and supplementing it with one of the texts you've mentioned simultaneously? If you read Rudin and find that you have a lot of questions, then use the supplements and this site; questions will only help you.
