AOUFI, khayra2020-11-172020-11-172020http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/20498In this work, we tackle Lipschitz space Lip0 (X), that X is a pointed metric space, and it is dual. We study the preduals Æ(X) and F (X), that are isometrics in addition to its properties. Then we study the space lip0 (X), which is under certain conditions of X is a predual of Æ(X). We end this work, by introducing B-Lipschitz summing operators.enMetric space, Lipschitz space, Arens-Eells space, Free Banach space, The little Lipschitz space, B-Lipschitz summing operators.Thesis