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 CharacteristicsReadership: Mathematicians.Key Features:Chapters are written by leading scientists such as Prof Gregoriadis, Prof Moghimi, Prof Kabanov, Prof Tomalia, Prof Couvreur, Prof Mueller, Prof Gabizon and Prof Kreuter