In this course, we are interested to the resolution of elliptical equations with various types of boundary conditions: Dirichlet, Neumann or Fourier-Robin, Navier or Navier type conditions. We will study the existence, the uniqueness and the regularity of the solutions. This regularity will depend, as we will see on data of the problem and in particular of the regularity of the domain. For the sake of clarity and simplification, we will examine two model problems, one involving the Laplacian and the other the Stokes operator.