  The auxiliary-field quantum Monte Carlo (AFQMC) method provides a
computational framework for solving the time-independent Schroedinger equation
in atoms, molecules, solids, and a variety of model systems by stochastic
sampling. We introduce the theory and formalism behind this framework, briefly
discuss the key technical steps that turn it into an effective and practical
computational method, present several illustrative results, and conclude with
comments on the prospects of ab initio computation by this framework.
