This talk is intended as an entry level introduction geometric singular perturbation theory (GSPT), which provides a modern approach to the study of singular perturbation problems arising in the form of multi-scale dynamical systems in a wide range of applications. First and foremost, I aim to show how the âsingularâ nature of multi-scale problems manifests itself geometrically, leading naturally to a geometric framework (and hence the âGâ in GSPT). Once a geometric viewpoint is developed, I will show by means of a straightforward application how fundamental results with roots in invariant manifold theory can be applied in order to draw meaningful conclusions about the dynamics of non-trivial singular systems, without recourse to matched asymptotics.