  Set-functions appear in many areas of computer science and applied
mathematics, such as machine learning, computer vision, operations research or
electrical networks. Among these set-functions, submodular functions play an
important role, similar to convex functions on vector spaces. In this tutorial,
the theory of submodular functions is presented, in a self-contained way, with
all results shown from first principles. A good knowledge of convex analysis is
assumed.
