Artificial intelligence has recently turned to formal logic in the search for powerful yet well-behaved knowledge representation languages. This book covers the background of classical logic, including the major meta-theorems, and the state of the art in theorem proving including Bibel's connection method. Also covered are the advanced adaptations of classical logic now being used in artificial intelligence - temporal and modal logics, reason maintainance and intensional logic. The book covers a wider range of topics than the currently available books in this area, and is more directly aimed at workers in artificial intelligence.