The development of the theory needed to classify degenerate critical points of smooth functions will be continued in Chapters 3–6. After that, the remaining six chapters are devoted to the local stability of smooth functions under small perturbations, a central aspect of Catastrophe Theory that is particularly important for applications. As a matter of fact, the name “catastrophe” was chosen for this theory because of its applications. In this chapter, stability will be treated heuristically by considering examples, in order to give an insight into the complete theory now and not to have to wait until the last six chapters.