"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 Faà 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.