This chapter introduces in full generality the central concept of this book, namely the notion of polygraph. Given an n-category, a cellular extension of it consist in attaching cells of dimension n+1 between certain pairs of parallel n-cells. This operation freely generates an (n+1)-category. Polygraphs are then obtained by starting with a set, considered as a 0-category and inductively repeating the above process in all dimensions. The construction yields a fundamental triangle of adjunctions between omega-categories, polygraphs, and globular sets. A brief description of (n,p)-polygraphs, that is, the notion of polygraph adapted to (n,p)-categories, concludes the chapter.