Inhalt: The course aims to give an introduction to classical singularity theory as initiated by H. Whitney (and later V. I. Arnold). We will study differentiable maps between manifolds and examine how they behave and degenerate in the vicinity of critical points. This uncovers a beautiful theory with connections to many different parts of mathematics and plenty of applications. In the beginning we look at some motivating examples, then set up a general theory to study them. This includes the introduction of tools from complex analysis, differential geometry and topology. If time permits we will discuss possible generalizations to the non-smooth setting or study some applications in the natural sciences, e.g. biology or physics.
