Abstract
Enumeration problems occupy a central place in Extremal Combinatorics. In this talk, I will survey classical results of this sort and go over some recent developments. In particular, I will discuss the problem of estimating the number of maximal sum-free sets in both integers {1,..,n} and finite abelian groups. Here, a set is called sum-free if it does not contain any solution to the equation x+y=z.
