I will give an introductory talk to the mathematical theory of black holes, which are special solutions of a differential geometric nature to the
Einstein field equations of general relativity. Many interesting questions can be asked about such solutions. In this talk, I will focus on the issue to what extent special solutions can be classified that are time-independent. It turns out that there is, in many cases, only a finite
dimensional family of solutions. The nature of the `parameters', or more properly, differential geometric invariants, that classify the solutions have in some cases amusing connections to certain structures and constructions in the theory of the `geometry of numbers', such as Farey trees. I will explain some of these.