Simultaneous normalization of families of isolated singularities

A singularity refers always to a special situation, something that is not true in general. The term ”singularity“ is often used in a philosophical sense to describe a frightening or catastrophically situation which is often unknown. Singularity theory in mathematics is a well defined discipline with the aim to tame the ”catastrophe“. I will give a general introduction to singularity theory with some examples from real life. Then I consider a special kind of taming a singularity, the normalization, and give an overview of classical and recent results on simultaneous normalization of families of algebraic and analytic varieties. I will also discuss some open problems.