This book is the result of several years of teaching experience at Grenoble INP (Ensimag). It is essentially self-instruction oriented, but of course can be used in traditional courses. Logic (propositional, first-order, and non-classical) plays a key role in Computer Science and Artificial Intelligence. A huge amount of information exists in different supports (such as books, articles, and web pages), but to avoid becoming lost in these references, the beginner needs a unified, synthetic approach. Such an approach is followed throughout the book, which surveys tableaux, resolution, Davis and Putnam methods, and logic programming along with unification and subsumption. For non-classical logics, the translation method is privileged. Numerous historical remarks and digressions concerning connections with other domains, as well as a plethora of exercises including detailed solutions, will accompany the reader in his learning.