The present work is not exactly a course , but rather is presented as a monograph in which the author has set forth what are, for the most part, his own results; this is particularly true of Chaps. 7-13. Many of the problems dealt with herein have, since the school year 1975-76, been the subject of a series of graduate lectures at the Universire des Sciences et Techniques de Lille I for students preparing for the Diplome d'Etudes Ap profondies de Mecanique (option fluides) . The writing of this book was thus strongly influenced by the author’s own conception of meteorology as a fluid mechanics discipline which is in a privi leged area for the application of singular perturbation techniques. It goes without saying that the modeling of atmospheric flows is a vast and complex problem which is presently the focal point of many research projects. The enonnity of the topic explains why many important questions have not been taken up in this work, even among those which are closely related to the subject treated herein. Nonetheless, the author thought it worthwhile for the development of future research on the modeling of atmospheric flows (from the viewpoint of theoretical fluid mechanics) to bring forth a book specifying the problems which have already been resolved in this field and those which are, as yet, unsolved.