This chapter provides a self-contained introduction to a collection of topics in computer science that focusses on the abstract, logical, and mathematical aspects of computing. First, mathematical structures called graphs are described that are used to model pairwise relations between objects from a certain collection. Second, abstract machines with a finite number of states called finite state automata are detailed. Third, mathematical models of computation are studied and their relationships to formal grammars are explained. Fourth, combinatorial logic is introduced, which describes logic circuits whose output is a pure function of the present input only. Finally, the degrees of complexity to solve a problem on a computer are outlined.