Let $M$ be a complete Riemannian manifold. My question is, under what conditions does $M$ admit a discrete group of isometries $\Gamma$ which acts properly discontinuously and cocompactly on $M$, that is, $M / \Gamma$ is a compact Riemannian manifold? If needed, one can assume that $M$ has negative (and even constant negative) curvature. This is mainly a reference request.