This textbook provides a first introduction to mathematical logic which is closely attuned to the applications of logic in computer science. In it the authors emphasize the notion that deduction is a form of computation. While all the traditional subjects of logic are covered thoroughly - syntax, semantics, completeness, and compactness - much of the book deals with less traditional topics such as resolution theorem proving, logic programming, and non-classical logics - modal and intuitionistic - which are becoming increasingly important in computer science. The book also provides a systematic treatment of the elements of set theory, a historical overview of its subjects, and an extensive annotated bibliography. No previous exposure to logic is assumed, and so this will be suitable for upper level undergraduate or beginning graduate students in computer science or mathematics.