"This is the second, improved edition of the only existing monograph devoted to real-analytic functions, whose theory is rightly considered in the preface 'the wellspring of mathematical analysis.' Organized in six parts, [with] a very rich bibliography and an index, this book is both a map of the subject and its history. Proceeding from the most elementary to the most advanced aspects, it is useful for both beginners and advanced researchers. —MATHEMATICAL REVIEWS "Bringing together results scattered in various journals or books and presenting them in a clear and systematic manner, the book is of interest first of all for analysts, but also for applied mathematicians and researchers in real algebraic geometry." —ACTA APPLICANDAE MATHEMATICAE

"The book can be highly recommended for graduate students as a comprehensive introduction to the field of geometric analysis. Also mathematicians working in other areas can profit a lot from this carefully written book. In particular, the geometric ideas are presented in a self-contained manner; for some of the needed analytic or measure-theoretic results, references are given."

First published in 2003, this is an accessible and thorough treatment of implicit and inverse function theorems and their applications. The book documents and places in context a substantial body of concepts that have played an role in modern mathematics.