In this chapter we introduce the basic framework of quantum computation as an abstract extension of the classical logic. Quantum logic gates and their quantum circuit representations are given. Applications to Bell state generation and Bell state measurement as well as to the quantum teleportation are provided. Furthermore, we address the Deutsch, the Deutsch–Jozsa and the Bernstein–Vazirani algorithms. We close the chapter with some considerations about the universality of single-qubit gates and CNOT and we state the Gottesman–Knill theorem concerning the efficient simulation of quantum computation on classical computers.