Preface to the English edition We are happy to welcome the English translation of our book, which origi- nally appeared under the title 'Operateurs pseudo-differentiels et theoreme de Nash-Moser' in 1991 (InterEditions/Editions du CNRS, Paris). Though the world of partial differential equations has changed a lot during these years, we think that the elementary presentation of the subjects touched upon in our book is still up to date and can be useful thus, we made no changes, except for correcting some misprints. On the other hand, several remarkable books on partial differential equations have appeared since: though their scopes largely exceed that of our book, we thought it relevant to mention them in our bibliography. Finally, we wish to thank the translator, Dr. Stephen S. Wilson, and the editorial board of the AMS, who worked to produce this new edition of our work. Orsay, November 2006 Serge Alinhac and Patrick Gerard Translator's note The numbering system I have used in my translation is essentially that employed by the authors in the original French edition so that the actual equation numbers etc. are the same in both versions. I did, however, make certain changes to the cross-referencing system: for example, to remove ambiguity, outside of Chapter II Exercise A.l of that chapter may be referred to here as Exercise II.A. 1 although within Chapter II it is referred to as Exercise A.l. Cheltenham, February 2007 Stephen S. Wilson vn

Purchased from American Mathematical Society for the exclusive use of nofirst nolast (email unknown) Copyright 2007 American Mathematical Society. Duplication prohibited. Please report unauthorized use to cust-serv@ams.org. Thank You! Your purchase supports the AMS' mission, programs, and services for the mathematical community.