In this chapter, we collect many results with a special view towards algebraic geometry over algebraically closed fields of positive characteristic. This includes construction techniques of algebraic varieties using group schemes, covers, and purely inseparable morphisms. We discuss rational double point singularities and after that, we turn to del Pezzo surfaces and two special subclasses, namely symmetroid surfaces. We discuss some general aspects of lattice theory and Picard schemes. We finally discuss various cohomology theories and give interpretations of cohomology groups of small degree. These results will be needed for the study of Enriques surfaces, but since many of these results are scattered over the literature and sometimes hard to find, we also provide references and give more background than needed later in the book.