1. Introduction 2. Numerical solution of linear systems 3. Finite element approximation 4. Polymonial approximation 5. Galerkin collocation and other methods 6. Elliptic problems approximation by galerkin and collocation methods 7. Elliptic problems approximation by mixed and hybrid methods 8. Steady advection diffusion problems 9. The stokes problems 10. The steady navier stokes problem 11. Parabolic problems 12. Unsteady advection diffusion problems 13. The unsteady navier stokes problem 14. Hyperbolic problems