I. Subdifferentiability and Duality Mappings -- ยง 1. Generalities on convex functions -- ยง 2. The subdifferential and the conjugate of a convex function -- ยง 3. Smooth Banach spaces -- ยง 4. Duality mappings on Banach spaces -- ยง 5. Positive duality mappings -- Exercises -- Bibliographical comments -- II Characterizations of Some Classes of Banach Spaces by Duality Mappings -- ยง 1. Strictly convex Banach spaces -- ยง 2. Uniformly convex Banach spaces -- ยง 3. Duality mappings in reflexive Banach spaces -- ยง 4. Duality mappings in LP-spaces -- ยง 5. Duality mappings in Banach spaces with the property (h) and (?)1 -- Exercises -- Bibliographical comments -- III Renorming of Banach Spaces -- ยง 1. Classical renorming results -- ยง 2. Lindenstraussโ{128}{153} and Trojanskiโ{128}{153}s Theorems -- Exercises -- Bibliographical comments -- IV On the Topological Degree in Finite and Infinite Dimensions -- ยง 1. Brouwerโ{128}{153}s degree -- ยง 2. Browder-Petryshynโ{128}{153}s degree for A-proper mappings -- ยง 3. P-compact mappings -- Exercises -- Bibliographical comments -- V Nonlinear Monotone Mappings -- ยง 1. Demicontinuity and hemicontinuity for monotone operators -- ยง 2. Monotone and maximal monotone mappings -- ยง 3. The role of the duality mapping in surjectivity and maximality problems -- ยง 4. Again on subdifferentials of convex functions -- Exercises -- Bibliographical comments -- VI Accretive Mappings and Semigroups of Nonlinear Contractions -- ยง 1. General properties of maximal accretive mappings -- ยง 2. Semigroups of nonlinear contractions in uniformly convex Banach spaces -- ยง 3. The exponential formula of Crandall-Liggett -- ยง 4. The abstract Cauchy problem for accretive mappings -- ยง 5. Semigroups of nonlinear contractions in Hilbert spaces -- ยง 6. The inhomogeneous case -- Exercises -- Bibliographical comments -- References