  The theory presented in this monograph establishes the first mathematically
rigorous result on the global nonlinear stability of self-gravitating matter
under small perturbations of an asymptotically flat, spacelike hypersurface of
Minkowski spacetime. It allows one to exclude the existence of dynamically
unstable, self-gravitating massive fields and, therefore, solves a
long-standing open problem in General Relativity. By a significant extension of
the Hyperboloidal Foliation Method they introduced in 2014, the authors
establish global-in-time existence for the Einstein equations expressed as a
coupled wave-Klein-Gordon system of partial differential equations. The metric
and matter fields are sought for in Sobolev-type functional spaces, suitably
defined from the translations and the boosts of Minkowski spacetime.
