1.Introduction. 2.Minimization of convex functionals. 3.Variational inequalities. 4.Transposition of operators.a pplications. 5.Sobolev spaces. 6.Examples of variational problems in one dimension. 7.Examples of variational problems in several dimensions. 8.Variational formulation of a Free-Boundary problem. 9.Fixed point theorems. 10.Some results on the existence of solutions of variational inequalities. 11.Quasivariatioal inequalities. 12.Free-Boundary problems. 13.Free-Boundry problems and variational inequalities. 14.Seminorms. 15.Regularization and partition of the unit. 16.On the regularity of the open sets. 17.The maximum principle and its applications. 18.On Green’s formulae. 19.Ordered structure. 20.Multi-Value mapping.