The book is devoted to new and classical results of the theory of linear partial differential operators in Gevrey spaces. The “microlocal approach” is adopted, by using pseudo-differential operators, wave front sets and Fourier integral operators. Basic results for Schwartz-distributions, c∞ and analytic classes are also included, concerning hypoellipticity, solvability and propagation of singularities. Also included is a self-contained exposition of the calculus of the pseudo-differential operators of infinite order. Contents:IntroductionGevrey Functions and UltradistributionsBasic Problems and Basic Operators in Gevrey ClassesPseudo-Differential OperatorsOperators with Multiple Characteristics Readership: Mathematicians. keywords:Mathematics;Mathematical Analysis;Partial Differential Equations;Pseudo-Differential Equations;Microlocal Analysis;Function Spaces;Gevrey Spaces;Hypoellipticity;Local Solvability;Multiple Characteristics “The book is well written, reasonably self-contained, gives a number of examples, and has an adequate bibliography.” SIAM Review “The book is a good introduction to the Gevrey microlocal analysis for students and post-graduate students, but it is also useful for all specialists working in the domain of the general theory of linear partial differential operators.” Mathematics Abstracts