On Cobham's theorem

In this chapter we essentially focus on the representation of non-negative integers in a given numeration system. The main role of such a system --- like the usual integer base $k$ numeration system --- is to replace numbers or more generally sets of numbers by their corresponding representations, {\em i.e.}, by words or by languages. First we consider integer base numeration systems to present the main concepts but rapidly we will introduce non-standard systems and their relationships with substitutions.