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I would like to continue my study of analysis, albeit temporarily in self-study, and I was wondering what would be the best "sequel" to baby Rudin. Thank you very much for your advice.

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Why not follow up with Rudin's Real and Complex Analysis? It contains real, complex and functional analysis all in one! Totally awesome!

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    Are you wrongly doing some conflating here? Baby Rudin = Principles of Mathematical Analysis; Papa Rudin = Real and Complex Analysis; Grandpa Rudin = Functional Analysis; source: Wikipedia article on Walter Rudin: https://en.wikipedia.org/wiki/Walter_Rudin2017-05-19
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I highly recommend Gerald Folland's Real Analysis: Modern Techniques and Their Applications, which is one of the most student-friendly analysis texts out there.

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    @User001: My personal opinion is that Royden is even friendlier and more elementary, whereas Folland assumes the reader is a little more mathematically mature. But Folland is more thorough (which I really appreciate), and I think ultimately provides students with a stronger background. I like both.2016-05-21