In this chapter we study another growth notion. For each conjugacy class C ⊆ G, we define the length of C as the minimal length of the elements of C. Recall that in Chapter 7 we were interested, given a, x ∈ G, in the displacement of x by a, i.e. the distance d(x, ax) = l(x-1ax) (the definition in Chapter 7 is slightly different). Fixing a, we can ask what is the minimal distance that it can displace any element of G, and we see that this is the length of the conjugacy class containing a. It is natural to count the number of classes of a given, or bounded length; the numbers cG(n) = cn, dG(n) = dn of classes of length n, or at most n, define the conjugacy growth functions of G. We include the value cG(0) = 1 (the subscript G will often be omitted; it will also often be convenient to write c(n), d(n), rather than cn, dn, etc.). These functions can behave very differently from the ordinary growth: e.g. there are infinite groups, of all cardinalities, and even finitely generated ones in which all nonidentity elements are conjugate, and thus cn = dn = 2 for all n. Other examples have more than two, but still a finite number, of classes. Like the ordinary growth function, the study of the conjugacy growth function has geometrical motivations; this study is much less developed than the one for ordinary growth.