This book grew out from a course that Masaki Kashiwara gave at the "Universite Paris-Mord" during the first term of the academic year 1976-77. Teresa Honteiro Fernandes worked out lecture notes for this course, which were preprinted in 1979 by Paris-Mord under the title "Systemes d'equations microdiffentielles" and distributed to a happy few. On the grounds that such a basic textbook should be made available to a wider mathematical audience, the Birkha'user Publishing Company proposed to make it a new volume of its series "Progress in Mathematics". Kashiwara and the publisher agreed not to change the overall structure of the text (which at first was supposed to be provisional); T. Monteiro Fernandes then was kind enough to take care of the translation into English and of the necessary minor corrections.

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