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Math. vol. 2, (1981), 365-397. 23. J. S. 3, (1974), 503-505. 24. L. Pontrjagin, Topological groups, Princeton University Press, fifth printing, 1958. 25. T. Robart, Groupes de Lie de dimension infinie. second et troisieme theoremes de Lie. ce, C. R. Acad. Sci. Paris, Serie I 322 (1996), 1071-1074. 26. T. Robart, Sur I'integrabilite des sous-algebres de Lie en dimension infinie, Can. J. , vol. 49 (4), 1997 pp. 820-839. 27. T. Robart, On Milnor's regularity and the path functor for the class of infinite dimensional Lie algebras of CBH type, Algebras, Groups and Geometries 16, 1998.

5 (1939), 794-805. 30 19. J. Milnor, Remark on infinite-dimensional Lie groups, Proceedings of les Houches' Summer School, session XL, pp. 1007-1057, North-Holland, 1984. 20. P. J. Olver, Applications of Lie groups to differential equations, Graduate texts in mathematics, vol. 107, Springer-Verlag, New York, 1993. 21. H. , vol. 427, Springer-Verlag, 1974. 22. H. Omori; Y. Maeda; A. Yoshioka; O. Kobayashi: On regular FrechetLie groups. Math. vol. 2, (1981), 365-397. 23. J. S. 3, (1974), 503-505.

Japan Acad. 63 Ser. A (1987). 24. , Groups and Group Functions Attached to Kac-Moody Data, Lecture Notes in Mathematics no. 1111 (1984), 193-223. edu We give a survey on the Lie group structures of pseudodifferential operators and Fourier integral operators together with their associated diffeomorphism groups. Our goal is to describe the case of open manifolds, but we first review the compact case and then outline the difficulties that arise for non-compact manifolds and show how we solved them.