On non-perturbative analysis of massive and bimetric gravity

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.