"This well-organized and clearly written advanced textbook introduces students to real analytic functions of one or more real variables. Many historical remarks, examples and references to the literature encourage the beginner to study further this ample, valuable and exciting theory." (1st ed.) New to the 2nd ed.: A more revised and comprehensive treatment of the Fa� di Bruno formula * An alternative treatment of the implicit function theorem * Topologies on the space of real analytic functions * The Weierstrass Preparation Theorem. Reference text for self-study or classroom.

Review

"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. Names such as Cauchy-Kowalewsky (Kovalevskaya), Weierstrass, Borel, Hadamard, Puiseux, Pringsheim, Besicovitch, Bernstein, Denjoy-Carleman, Paley-Wiener, Whitney, Gevrey, Lojasiewicz, Grauert and many others are involved either by their results or by their concepts."

―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

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