The Nash-Moser inverse mapping theorem
Journées équations aux dérivées partielles (1983), article no. 11, 6 p. 
@incollection{JEDP_1983____A11_0,
     author = {Masatake Kuranishi},
     title = {The {Nash-Moser} inverse mapping theorem},
     booktitle = {},
     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {11},
     pages = {1--6},
     publisher = {\'Ecole polytechnique},
     year = {1983},
     zbl = {0516.58009},
     mrnumber = {719236},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/item/JEDP_1983____A11_0/}
}
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Masatake Kuranishi. The Nash-Moser inverse mapping theorem. Journées équations aux dérivées partielles (1983), article  no. 11, 6 p. https://proceedings.centre-mersenne.org/item/JEDP_1983____A11_0/

[1] : R. Hamilton : “The inverse function theorem of Nash and Moser”. Bulletin of the Amer. Math. Soc., vol. 7, N° 1 (1982) 65-222. | MR | Zbl

[2] : M. Kuranishi : “Strongly pseudoconvex CR structures over small balls”. I. Ann. of Math. 115 (1982), 451-500, II. Ann. of Math. 116 (1982), 669-732, III. Ann. of Math. 116 (1982). | MR | Zbl

[3] : J. Moser : “A new technique for the construction of solution of non-linear differential equations”. Proc. Nat. Acad. Sci. 47, N° 11 (1961), 1824-1831. | MR | Zbl