The purpose of this new book will be to provide a detailed illustration of the most recent developments for the theory of the SGpsuedodifferential operators a class of operators introduced by Parenti and Cordes in the 70's. This book will deal with the main aspects of global calculus of pseudo differential operators on Rn and on manifolds with conical /cylindrical ends. Many of the books now out on this topic do not cover some of the most recent achievements in this field. It is especially true for the results on manifolds with ends and on wave front sets, propagation properties and parabolic problems. This book will make it easier for the many researchers in the field to learn more about the study of this topic.