  We discuss the fully non-linear formulation of multigravity. The concept of
universality classes of effective Lagrangians describing bigravity, which is
the simplest form of multigravity, is introduced. We show that non-linear
multigravity theories can naturally arise in several different physical
contexts: brane configurations, certain Kaluza-Klein reductions and some
non-commutative geometry models. The formal and phenomenological aspects of
multigravity (including the problems linked to the linearized theory of massive
gravitons) are briefly discussed.
