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Mathematical logic is an important basis for mathematics, computer Science, and artificial intelligence. The application of logic as a problem-solving tool is an important aspect of education of computer scientists and engineers. This book provides a comprehensive introduction to various logics, including the classical propositional logic and first-order predicate logic, as well as equational logic, temporal logic, and Hoare logic. The focus of the book is to present algorithms in the form of proof procedures for the classical logics and decision procedures for checking the satisfiability of logical formulas. A large portion of the book is devoted to the introduction of software tools based on these algorithms and the practical problems which can be solved by these tools in constraint satisfaction, formal verification, and artificial intelligence. The book assumes no background in logic. It is appropriate for (junior and senior) undergraduate and graduate students majoring in computer science or mathematics. Each chapter has about a dozen or so exercises to help the reader understand the materials.