BOUATIA, Salim2019-07-282019-07-282019http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/15990Let X a pointed metric space, and Lip(X) the Lipschitz space. By the theorem of Diximer Lip0 (X) = X# is a dual. We are built the space of Arens Eells Æ(X) which is the predual of X# . Then we are interested in the other construction due to Johnson who is noted by Godfroy and Kalton by F(X). We ending this memory by proof that Æ(X) ≡ F(X ) by Pestov’s theorem.enMetric pointed, Arens Eells space, Lipschitz space , free Lipschitz space.Thesis