1. Motivation for the study of singular perturbation problems -- 2. Simple examples of singular perturbation problems -- 3. Numerical methods for singular perturbation problems -- 4. Simple fitted operator methods in one dimension -- 5. Simple fitted mesh methods in one dimension -- 6. Convergence of fitted mesh finite difference methods for linear reaction-diffusion problems in one dimension -- 7. Properties of upwind finite difference operators on piecewise uniform fitted meshes -- 8. Convergence of fitted mesh finite difference methods for linear convection-diffusion problems in one dimension -- 9. Fitted mesh finite element methods for linear convection-diffusion problems in one dimension -- 10. Convergence of Schwarz iterative methods for fitted mesh methods in one dimension -- 11. Linear convection-diffusion problems in two dimensions and their numerical solution -- 12. Bounds on the derivatives of solutions of linear convection-diffusion problems in two dimensions with regular boundary layers -- 13. Convergence of fitted mesh finite difference methods for linear convection diffusion problems in two dimensions with regular boundary layers -- 14. Limitations of fitted operator methods on uniform rectangular meshes for problems with parabolic boundary layers -- 15. Fitted numerical methods for problems with initial and parabolic boundary layers