This book gives a standard first course in propositional and predicate logic. No prior knowledge of the subject is needed to read the book. The basic material is concentrated in chapter 3 (propositional logic), chapter 5 (quantifier-free logic) and chapter 7 (first-order logic, including completeness and compactness). Chapter 8 contains deeper results, in particular Church undecidability, Gödel undecidability and the incompleteness theorems. The proofs are based on Matiyasevich’s theorem, formulated in 5.8.6 using the notions of computable and computably enumerable sets stated in 5.8.4 on an intuitive (but acceptable) level. Chapters 1, 2, 4 and 6 contain the motivation and a discussion of formal and psychological aspects of logic considerations in applications. Many examples and exercises are included. Moreover, appendix B provides some information on denotational semantics. The book is written on the foundation of the extensive teaching experience of the authors. They have succeeded in giving a presentation of the subject in a formally correct and intuitively acceptable way. They also include some applications in computer science and linguistics.