Real Analysis Textbook Recommendation

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Recommendations for self-studying real analysis include considering Apostol's "Mathematical Analysis," especially for those who have completed Apostol's "Calculus, Vol. 2." Other popular texts mentioned are Rudin, Pugh, and Abbott, with Rudin noted as a common choice but potentially challenging for self-study. Abbott is highlighted for its clear explanations, making it suitable for beginners. The discussion suggests a progression from Abbott to Rudin, particularly for those who have successfully tackled problems in Apostol. Overall, the consensus leans towards starting with Abbott for a solid foundation before advancing to Rudin.
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Does anyone have a recommendation for a book(s) to use for the self-study of real analysis? I have just finished Apostol Calculus, Vol. 2 and would like to move on to real analysis. I am not sure whether I should continue following Apostol and move on to Apostol mathematical analysis or something else. I have been looking at other real analysis books such as Rudin, Pugh, and Abbott. I know that Rudin is the most used textbook, but I'm not sure it's suited for self-study. My current plan is to do Abbott and then move on to Rudin. Would this be a good course of action?
 
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Abbot is good for self study. Really helpful explanations.

But since you did Apostol. Do you mean solved the majority of the problems without looking them up online? Etc. if you did do this. Then I think you are ready for Rudin.
 

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