This books it's exactly what I'm looking for: I want/need to do the jump from calculus, Lin-Algebra, PDEs to further topics like Integral Equations.  Those are formulated on the more abstract grounds of Hilbert Spaces (i.e infinite dimensional vector spaces), to go there I must (willingly) detour to Real Analysis, which in turns requires mathematical proofs, and that's why I acquired this title, influenced mostly from the video about it, here in Amazon<br><br>For me the wining point is the style on which the book is written:  introductory, intuitive, chatty:  not too  terse, not too wordy;  telling you what is going on between lines, and where concepts come from and to where they are heading<br><br>I'm writing this just after reading those first 20 pages, and I'm excited about for what is yet to come!<br>I will be reporting more as I advance. I will definitely purchase the author's other book on Real Analysis<br><br>Upgrade after completing Chapter 4<br> I'm working out in detail the text and the problem sets. My opinion of the book hasn't changed. It's a great book.