Abstract Chapter 2 provides a review of pertinent aspects of the quantum mechanics of systems composed of many particles. It focuses on the foundations of quantum many-particle physics, the many-particle Hilbert spaces to describe large assemblies of interacting systems composed of Bosons or Fermions, which lead to the versatile formalism of second quantization as a convenient and eminently practical language ubiquitous in the mathematical formulation of the theory of many-particle systems of quantum matter. The main objects in which the formalism of second quantization is expressed are the Bosonic or Fermionic creation and annihilation operators that become, in the position basis, the quantum field operators.