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We discuss the fully non-linear formulation of multigravity. The concept ofuniversality classes of effective Lagrangians describing bigravity, which isthe simplest form of multigravity, is introduced. We show that non-linearmultigravity theories can naturally arise in several different physicalcontexts: brane configurations, certain Kaluza-Klein reductions and somenon-commutative geometry models. The formal and phenomenological aspects ofmultigravity (including the problems linked to the linearized theory of massivegravitons) are briefly discussed.Comment: 41 pages, 4 Figures, final version to be published in Phys.Rev.

Effective Lagrangians and universality classes of nonlinear bigravity