An elementary introduction to formal logic, particularly intended for linguists and others interested in languages. Concepts and theories developed within formal logic for the study of artificial languages have for some time been fruitfully applied to the study of natural languages, and some knowledge of them is now necessary for students of linguistics (especially semantics). With this need in mind the authors offer a clear, succinct and basic introduction to set theory, inference, propositional and predicate logic, deduction, modal and intensional logic, and various recent extensions of these. There is a discussion too of the relation between linguistics and logical analysis and between logic and natural language. The authors see increasing scope for cooperation between logicians and linguistics in studying the structure of language, and it is the overall aim of the book to promote this cooperation.