This book appears in the series Oxford Graduate Texts in Mathematics, and can be used in an advanced undergraduate course or a graduate course in Analysis. It contains the main topics in Analysis arranged in ten chapters, followed by two chapters of "applications" covering Probability and Distributions.
Since it contains so many important topics, is written very well, with complete proofs and explanations, this book is a very valuable contribution to the wide and beautiful field of “modern analysis.” It was developed by the author over many years (since 1964) of teaching analysis courses at several universities.
One more reason to strongly recommend this book: it has solutions to the many exercises at its companion website: http://www.oup.com/uk/booksites/content/0199203156/
Mihaela Poplicher is associate professor of mathematics at the University of Cincinnati. Her research interests include functional analysis, harmonic analysis, and complex analysis. She is also interested in the teaching of mathematics. Her email address is Mihaela.Poplicher@uc.edu.