From the very beginning and still today, telecommunications theory has relied on classical physics and rules of classical systems. However, telecommunications actually obeys the more general postulates and laws of quantum mechanics. In order to fully understand the advantage quantum mechanics provides to telecommunications, it is important to start by encompassing the fundamental definitions and theories of this field of physics. This chapter reviews preliminaries, notations, and terminologies of quantum mechanics that are pivotal to understanding the theory of quantum communication networks. Such content is introduced and explained, suitable for readers with a background either in physics or engineering. Beginning with Dirac notation, pure systems, composite systems, density matrices, entanglement, and quantum measurement models, the discussion next moves to quantum channels, statistical theory and quantum entropy. Finally, we explain the concept of quantum nonlocality and its connection to cooperative games in quantum game theory.