"Basler Lehrbücher" is a series of advanced mathematics textbooks, with Volume 4 titled "A Primer of Real Analytic Functions" edited by Herbert Amann and Hanspeter Kraft. The book is authored by Steven G. Krantz and Harold R. Parks. It provides an introduction to the theory of real analytic functions, covering both elementary and advanced topics. The book includes detailed discussions on basic properties of power series, analytic continuation, composition of analytic functions, inverse functions, and real analytic functions of several variables. It also addresses more complex topics such as Puiseux series, separate real analyticity, and the FBI transform. The text includes a comprehensive overview of classical topics like the theorem of Pringsheim and Boas, Besicovitch's theorem, and Whitney's extension and approximation theorems. Additionally, it explores results motivated by partial differential equations, including the division of distributions and the Paley-Wiener theorem. The book also covers geometric topics such as resolution of singularities, Lojaciewicz's structure theorem for real analytic varieties, and the embedding of real analytic manifolds. The authors aim to provide a clear and accessible introduction to the subject, highlighting the importance and diversity of the literature on real analytic functions. The book is intended for mathematicians and students interested in the theory of real analytic functions, offering a comprehensive overview of the field. The authors thank various colleagues for their contributions and acknowledge the responsibility for any remaining errors. The book is published by Springer Basel AG and includes a bibliography and index."Basler Lehrbücher" is a series of advanced mathematics textbooks, with Volume 4 titled "A Primer of Real Analytic Functions" edited by Herbert Amann and Hanspeter Kraft. The book is authored by Steven G. Krantz and Harold R. Parks. It provides an introduction to the theory of real analytic functions, covering both elementary and advanced topics. The book includes detailed discussions on basic properties of power series, analytic continuation, composition of analytic functions, inverse functions, and real analytic functions of several variables. It also addresses more complex topics such as Puiseux series, separate real analyticity, and the FBI transform. The text includes a comprehensive overview of classical topics like the theorem of Pringsheim and Boas, Besicovitch's theorem, and Whitney's extension and approximation theorems. Additionally, it explores results motivated by partial differential equations, including the division of distributions and the Paley-Wiener theorem. The book also covers geometric topics such as resolution of singularities, Lojaciewicz's structure theorem for real analytic varieties, and the embedding of real analytic manifolds. The authors aim to provide a clear and accessible introduction to the subject, highlighting the importance and diversity of the literature on real analytic functions. The book is intended for mathematicians and students interested in the theory of real analytic functions, offering a comprehensive overview of the field. The authors thank various colleagues for their contributions and acknowledge the responsibility for any remaining errors. The book is published by Springer Basel AG and includes a bibliography and index.