Distributions and Sobolev spaces -- Operators in Banach spaces -- Examples of boundary value problems -- Semigroups and laplace transform -- Homogenization of second order equations -- Homogenization in elasticity and electromagnetism -- Fluid flow in porous media -- Vibration of mixtures of solids and fluids -- Examples of perturbations for elliptic problems -- The Trotter-Kato theorem and related topics -- Spectral perturbation. Case of isolated eigenvalues -- Perturbation of spectral families and applications to selfadjoint eigenvalue problems -- Stiff problems in constant and varialbe domains -- Averaging and two-scale methods -- Generalities and potential method -- Functional methods -- Scattering problems depending on a parameter.