ADM analysis and massive gravity

Abstract: This is a contribution to the Proceedings of the 7th Mathematical Physics Meeting: Summer School and Conference on Modern Mathematical Physics, held in Belgrade 09 -- 19 September 2012. We give an easily accessible introduction to the ADM decomposition of the curvature components. After that we review the basic problems associated with attempts of constructing a viable massive gravity theory. And finally, we present the metric formulations of ghost-free massive gravity models, and comment on existence problem of the matrix square root.