Originally published in French as Analyse fonctionelle, théorie et applications (Paris: Masson, c1983) ; this English edition contains revisions and added exercises.

Includes bibliographical references (p. 585-594) and index.

The Hahn-Banach theorems : introduction to the theory of conjugate convex functions -- The uniform boundedness principle and the closed graph theorem -- Weak topologies, reflexive spaces, separable spaces, uniform convexity -- Lp spaces -- Hilbert spaces -- Compact operators, spectral decomposition of self-adjoint compact operators -- The Hille-Yosida theorem -- Sobolev spaces and the variational formulation of boundary value problems in one dimension -- Sobolev spaces and the variational formulation of elliptic boundary value problems in N dimensions -- Evolution problems : the heat equation and the wave equation -- Miscellaneous complements