Don't let the title fool you. This book will take you from sophomore real analysis through the first year of graduate analysis, covering set theory, topology, functionals, integration, and differentiation. This stands out as one of the best math books on my shelf.
I reciently graduated with a degree in math and physics. I liked this subject matter of this book for two reasons. First it is a good extension of the analysis I learned as an undergraduate. Second it puts the math(functionals, opperators, ...) used in physics classes such as quantum mechanics on a firm base. It also treats modestly applied problems such as existance and uniqueness of diff eq's which I have not seen in the limited number of other texts I have perused. I found the text to be extremely readable as far as intermediate analisys texts go. I highly recomend this to anyone with some background in analisys, or to physics students who want to know more about the math they use.
The only reason why I did not give it 5 stars is because it contains aboslutely no clue about most of the problems. Some people might argue that this forces you to go through the problems rather than to look at the solution at the first signs of failure. I beg to differ, I think that solutions help greatly to those who are learning by themselves be it for the first time or to gain a sounder knowledge of the subject (the latter is my case) and provide with good examples of rigour. One is always free to think of alternative ways, or maybe only solutions to odd (or even) exercises could have been included (As Kreyszig did on his book on Functional Analysis). Apart from this, I liked the book very much, written in the usual russian style. I would have liked it to include more material on spectral theory of operators however. I would certainly reccommend this book. Maybe not for beginner on the subject (for this I would go for Kreyszig's without doubt) but certainly for someone who has been exposed to Functional Analysis at some point and wishes to review or simply study it in more depth.
I studied maths at university some years ago and have kept on reading sporadically since. This is quite possibly the clearest, easiest to read maths book I have ever read. It does cover a lot of material fairly quickly (more than the title might suggest) but never feels rushed and the logical structure of the book makes perfect sense.
you rarely get a chance to read an introductary text by a master, Kolmogorov is one of 20th century's greatest mathematician, who is solely responsible for the foundatioin of modern probability theory. and the text exhibits Kolmogorov's typical style: authority and accessibility, it's truly under priced.
I dealt with Functional Analysis while attending a Mathematical Engeneering faculty, so my background was close to the one of an applied mathematician. This book was awesome in introducing to an almost completely new field. Clear and accessible and a good reference still today.