  We stabilize the full Arthur-Selberg trace formula for the metaplectic
covering of symplectic groups over a number field. This provides a
decomposition of the invariant trace formula for metaplectic groups, which
encodes information about the genuine $L^2$-automorphic spectrum, into a linear
combination of stable trace formulas of products of split odd orthogonal groups
via endoscopic transfer. By adapting the strategies of Arthur and
Moeglin-Waldspurger from the linear case, the proof is built on a long
induction process that mixes up local and global, geometric and spectral data.
As a by-product, we also stabilize the local trace formula for metaplectic
groups over any local field of characteristic zero.
