  The numerical analysis of stochastic parabolic partial differential equations
of the form $$ du + A(u) = f \,dt + g \, dW, $$ is surveyed, where $A$ is a
partial operator and $W$ a Brownian motion. This manuscript unifies much of the
theory developed over the last decade into a cohesive framework which
integrates techniques for the approximation of deterministic partial
differential equations with methods for the approximation of stochastic
ordinary differential equations. The manuscript is intended to be accessible to
audiences versed in either of these disciplines, and examples are presented to
illustrate the applicability of the theory.
