This logically self-contained introduction to analysis centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration. From the "This material can be gone over quickly by the really well-prepared reader, for it is one of the book’s pedagogical strengths that the pattern of development later recapitulates this material as it deepens and generalizes it." --AMERICAN MATHEMATICAL SOCIETY
This was my undergrad real analysis textbook. I don't like real analysis, and I don't like this book. But compared with Rudin's text principles of mathematical analysis it is quite good. If anything this book is not deep enough, but it is a good reference, and I have used it repeatedly since I finished the class.
It is a great book. Straight to the point and includes some topics that other books don´t. I used through my first class of analysis, and was a great choice.