g with Dirac notation, a formalism that is not only very elegant but is relatively simple to handle. The introduction of Dirac notation makes it possible to become familiar with the inner product for quantum states, as well as different properties for operators and states concerning projection, change of basis, unitary transformations, matrix elements, similarity transformations, eigenvalues and eigenstates, spectral decomposition and diagonal representation, matrix trace and density operator or matrix. The concept of density matrix makes it possible to provide a very first and brief hint of the analog of Shannon's entropy in the quantum world, referred to as von Neumann's entropy, to be further developed in Chapter 21. Once we have all the required tools, we can focus on quantum measurement and analyze three different types referred to as basis-state measurements, projection or von Neumann measurements, and POVM measurements. In particular, POVM measurements are shown to possess a remarkable property of unambiguous quantum state discrimination (UQSD), after which it is possible to derive "absolutely certain" information from unknown system states. The more complex case of quantum measurements in composite systems described by joint or tensor states is then considered. Although of a more abstract and formal character than any previous ones, this chapter is crucial to the understanding of the rest of these chapters, which are concerned with the manipulation of qubits. This is not only because of the importance of being comfortable with the Dirac formalism, but also of the need to have conceptually assimilated the basics of quantum measurement. Dirac notation In this section, I shall introduce so-called Dirac notation, which are used in quantum mechanics. When compared with the basic math formalism used in engineering, Dirac notation looks quite esoteric, if not highly involved and complex. But as we shall see, such notation is straightforward to assimilate, and quite easy to handle after familiarization. Dirac not