Computability theory is concerned primarily with determining what tasks can be accomplished by idealized computer programs. Formal language theory deals primarily with the ability of certain grammars to express the syntax of various types of languages. Both fields are branches of formal mathematics. The former theory has its roots in mathematical logic, the latter in mathematical linguistics which includes the mathematical theory of compiler design. In recent years, these two subjects have been studied extensively by computer scientists and have interacted to the point where, from the perspective of a computer scientist, they are frequently viewed as a single unified subject. As such, they have become a standard course topic in many computer science curricula. This book contains an introduction to these two interrelated subjects. It is suitable for an introductory course at either the advanced undergraduate or beginning graduate level. It also can be read and understood, without the aid of an instructor, by anybody who has either a background in theoretical mathematics or a reasonable amount of programming experience and some exposure to mathematical proofs.