Introductory Real Analysis (Dover Books on Mathematics) Paperback – 2 Jan. 2000

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.

Great book. Helped me a lot

... it is a must if you want to get an excellent introduction to the subject.

...is like staring at a painting of Rembrandt.

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.

The book is generally good. However, it has several mistakes, sometimes in the definitions, sometimes in the proofs. It is a good idea to have other books in the subject to consult.