Context-free grammars represent language-generating rewriting systems. Each of their rewriting rules has a single symbol on its left-hand sides. By repeatedly applying these rules, these grammars generate sentences of their languages. This chapter gives a mathematical introduction into context-free grammars. First, Section 6.1 defines their basic versions. Then, Section 6.2 presents several mathematical methods that transform the basic versions so that the transformed versions are as powerful as the original versions but are much easier to handle in theory as well as in practice.