Need help finding graduate analysis book

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Rudin's texts are widely regarded as foundational in real analysis, but their level can be challenging for some students. For graduate-level real analysis, Royden's "Real Analysis" is recommended, covering essential topics such as the Real line, Metric spaces, Topological spaces, Lebesgue integration, Banach spaces, and Measure theory, although it does not include complex analysis. For those looking to delve into complex analysis, Gamelin's book is suggested as it effectively covers a comprehensive course in the subject. The discussion highlights the importance of selecting the right texts to prepare for advanced studies in analysis, given the broad scope of the subject.
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I have just taken real analysis I and II (single and multivariable respectively) as an undergrad. I am planning on taking the grad analysis course next year.

From what I gather Rudin seems to be the time-tested bible of analysis, but I don't know at what level the book is written. Can anyone recommend a graduate level real analysis book?

Also, I am looking to get a head start on complex analysis, so if anyone could share the name of a good complex analysis text, I would appreciate it.

Thanks
 
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Please elaborate on the course. What are the subjects treated? Analysis is a big subject. Rudin already has three textbooks (principles, real and complex, functional) on analysis.
 
Royden's Real Analysis is a classic and features chapters on the Real line, Metric spaces, Topological spaces, Lebesgue integration, Banach spaces, and Measure theory. It doesn't feature complex analysis, however. Complex analysis by Gamelin is a good book and covers a year long course in the subject (or more or less depending on what you know).
 
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