Preliminaries -- Regular and Singular Perturbations -- Evolution Equations in Hilbert Spaces -- Singularly Perturbed Hyperbolic Problems -- Presentation of the Problems -- Hyperbolic Systems with Algebraic Boundary Conditions -- Hyperbolic Systems with Dynamic Boundary Conditions -- Singularly Perturbed Coupled Boundary Value Problems -- Presentation of the Problems -- The Stationary Case -- The Evolutionary Case -- Elliptic and Hyperbolic Regularizations of Parabolic Problems -- Presentation of the Problems -- The Linear Case -- The Nonlinear Case.