This document describes means for computing a number of information-theoretic properties of languages and their grammars. For example, the entropy of a system of symbols is widely recognized as a measure of that system's complexity and organization. It is shown how the entropy of a language can be computed in a simple way from a grammar annotated with production probabilities. The author then develops means for statistically estimating these production probabilities from measureable properties of strings in the language. He also considers the computation of other information theoretic properties of language and grammars, such as the average information born by a symbol in a language and the average information used by the productions of a grammar. (Author)