The Delta Method, also known as the Method of Propagation of Errors, refers to applications of the result that a smooth function of an asymptotically normal estimator also has an asymptotic normal distribution. The delta method has two principal groups of applications, first to the computation of a variance stabilizing transformation, and second to the computation of the asymptotic variance and confidence intervals for a nonlinear function of a set of previously estimated parameters, typically by the method of maximum likelihood. This article discusses the proof of both the univariate and multivariate versions of the theorem and gives numerous examples.