The theory of sets of finite perimeter provides, in the broader framework of Geometric Measure Theory, a particularly wellsuited framework for studying the existence, regularity, and structure of singularities of minimizers in those geometric variational problems in which surface area is minimized under a volume constraint. To this end, the class of sets of finite perimeter satisfy these requirements: 1. a class F of sets E ⊂ Rn endowed with a topology with good compactness properties so that sets with smooth boundaries belong to this class and are dense; 2. a notion of perimeter P (E) for every E ∈ F so that E → P (E) is lower- semicontinuous on F, and P extends the usual notion of perimeter Hn−1 of the boundary ∂E; more precisely we require that P (E) = Hn−1(∂E) for every set E with smooth boundary and for every E ∈ F there exists a sequence Eh → E with smooth boundaries and satisfying Hn−1(∂Eh) → P (E).