This research monograph deals with fast stochastic simulation based on im- portance sampling (IS) principles and some of its applications. It is in large part devoted to an adaptive form of IS that has proved to be effective in appli- cations that involve the estimation of probabilities of rare events. Rare events are often encountered in scientific and engineering processes. Their charac- terization is especially important as their occurrence can have catastrophic consequences of varying proportions. Examples range from fracture due to material fatigue in engineering structures to exceedance...