In this chapter we derive the foundational principles of statistical mechanics, as obtained by the density operatorDensity operator dynamics within a proper statistical ensemble. We first introduce the canonical ensembleCanonical ensemble deriving its statistics and corresponding thermodynamics, illustrating the canonical ensembleCanonical ensemble special case corresponding to the microcanonical ensembleMicrocanonical ensemble. We then derive the isothermal–isobaric and grand-canonical ensembleGrand-canonical ensemble statistics and thermodynamics, comparing the different ensembles and discussing the conditions ensuring the same thermodynamics regardless of the ensemble used.