  This is my contribution to Proceedings of II Russian-Spanish Congress on
Particle and Nuclear Physics at all Scales and Cosmology, Saint Petersburg,
Russia, October 1 - 4, 2013. We give a brief overview of the ghost-free massive
and bimetric gravity emphasising its non-perturbative aspects and ADM approach
to calculating the precise number of degrees of freedom. To the standard
material, we add some thoughts concerning existence and uniqueness problems of
matrix square roots in non-perturbative metric formulations of massive gravity.
