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The present work originates in a course given by the authors during the last few years in various university departments and institutions, among which we should like to mention: the Centre de Linguistique Quantitative of the Faculte des Sciences de Paris, created at the instance of the late Professor Favard; the Chaire d'Analyse Numerique of the Faculte des Sciences de Paris (Professor Rene de Possel), curriculum of Troisieme Cycle; the Chaire de Physique Mathematique of the University of Toulouse (Professor M. Laudet), for the degree DiplOme d'Etudes Approfondies in the section "Traitement de I'Information"; the department 1 of linguistics of the University of Pennsylvania (Professor Z. S. Harris); Institut de Programmation of the Faculte des Sciences de Paris for the troisieme niveau. the courses in the Written for purely didactic purposes, this Introduction to Formal Grammars makes no pretense to any scientific originality. Large portions of it have been borrowed from the fundamental and "classic" works cited in the bibliography, such as that of M. Davis, Computability and Unsolvability [9], and those of N. Chomsky, among others Formal Properties of Grammars [6]. Ineluctably, there are numerous borrowings made during a course, and the authors would like to acknowledge their debt to J. Pitrat for his lectures given in the Centre de Linguistique Quantitative mentioned above, and to M. Nivat for his work in connection 2 and transduction.