The preceding formulation of statistical mechanics is perhaps the simplest application of probability theory to the many-body problem. Although it is consistent with the principles of quantum mechanics, it is not manifestly so. That is, the PME itself is based on the notions of information and measurement, but a general formulation should also incorporate explicitly the quantum-mechanical theory of measurement. The present chapter is directed toward this generalization, beginning with a brief review of some selected formal aspects of quantum mechanics.