A decision procedure is an algorithm that, given the decision problem, ended up with the correct answer yes / no. The authors introduce the basic terminology of satisfiability modulo theories and then, in separate chapters, making the study procedures for each of the following theories: propositional logic; equalities and uninterpreted functions, linear arithmetic, bit vectors, arrays, pointers logic, and the formula is measured . They also study the problem of the theory of joint and decided to dedicate this chapter to modern techniques based on the interaction between the SAT solver and a decision procedure for the theory under investigation. This book has been used to teach undergraduate and graduate programs at ETH Zurich, at the Technion, Haifa, and at Oxford University.