In this chapter we provide prerequisites from several topics, like Riemann surfaces, braids and mapping classes, as well as Teichmüller theory. For completeness and convenience of the reader and for fixing notation and terminology we give here a recollection of basic facts, that will be used later frequently. References to the literature are given. In some cases proofs are included, for instance, in the case when the material is less standard and not extensively treated in the literature, or when the idea behind a statement will occur to be important in the following. Readers who are familiar with the material may skip this chapter and consult it later for notation and for some less standard facts that are include in this chapter.