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I am a first-year Math undergraduate and have been searching online for books in Analysis and have found two which seem to be good for an introduction.

  1. Ross' Elementary Analysis:The Theory Of Calculus.
  2. Abbott's Understanding Analysis.

I did a quick skim at the content and it seems that Abbott's Understanding Analysis has more content（breadth) but Ross' seems to go deeper?

I am not sure which book to choose (self-study) and any other recommendations/suggestions are welcome and highly appreciated!

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    Rudin's Principles – Amaan M Jan 28 '21 at 08:25
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    @AmaanM I strongly disagree with that recommendation. As much as a love baby Rudin, it is a terrible book to learn from, seemingly written with an expert audience in mind, rather than a novice student. There are numerous more modern texts which cover the same ground in a more approachable manner. Personally, I'm rather partial to the Princeton series written by Stein and Shakarchi. Tao's book is good, too. In any event, this question has been asked-and-answered quite a bit on this site before... – Xander Henderson Feb 03 '21 at 13:28
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    That's fair, I enjoyed baby Rudin during my first analysis course, but that was also in the context of taking a class, not self-study. I'll look into the ones you mentioned, thanks for the tips! – Amaan M Feb 03 '21 at 16:30

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  • Real Analysis By S Kumaresam. It is very comprehensive, but it covers only some topics.
  • Mathematical Analysis by Rudin. However, this is a little bit tough.
  • Mathematical Analysis by Tom Apostal. This one is best.
  • Introduction to Real Analysis Book by Robert G. Bartle Very comprehensive book, good for beginners.
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  • Bartle also has a great book on measure theory (I think it's just called "Integration"). I taught out of Ross once and hated it although I can't fully articulate why. The best I might do: if Rudin is maybe too close to how an expert sees analysis (which I agree that it probably is), Ross is too close to how you'd present analysis if the only point of doing analysis was to do homework assignments. Bartle is better than that. – leslie townes Feb 05 '21 at 05:14