TITLE: Real Analysis advanced book suggestion
QUESTION [8 upvotes]: I want to self study real analysis. So far, finished the first seven chapters of Baby Rudin (up to and including sequences and series of functions) and now want to proceed into more advanced books.
I have couple options, including

Stein&Shakarchi
Folland
Royden
Rudin's Real&Complex Analysis
Kolmogorov-Fomin

Among these five (also happy to hear if you have further recommendations) which are more accessible and has better treatment of the material? I'm especially thinking among first three, so if there would be a comparative answer for the first three books, I would be really happy. Any help is appreciated. Thank you!

REPLY [3 votes]: I’m studying real analysis in Ukraine, so I use a local set of books. The main of them I found at home when I was a child, and still hoping to completely read someday, is a fundamental, very detailed and so huge (it has more than two thousands pages in three volumes) book “Differential and Integral Calculus” by Grigorii Fichtenholz. This is a famous book for our students, and, according to Wikipedia,

The bookwas translated, among others, into German, Chinese, and Persian however a translation to English language has not been done still.


Fichtenholz's books about analysis are widely used in Middle and Eastern European as well as Chinese universities due to its exceptionality of detailed and well-ordered presentation of material about mathematical analysis. Due to unknown reasons, these books do not have the same fame in universities in other areas of the world.

Another book is “Mathematical analysis” by A.Ya. Dorogovtsev, with more modern (1993-4) and brief (only two small volumes with a bit more than six hundred pages in total) approach.