Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We describe, in a short overview, the construction of a Non equilibrium Statistical Mechanics Ensemble Formalism, providing a thermo-statistical theory of kinetic and relaxation processes. Such construction has been approached along the recently past 20th century by a pleiad of distinguished scientists, a work that can be subsumed in a large systematization in the form of a physically sound, general and useful, theoretical framework. We briefly comment on the main questions associated to that construction. Among them are the relevant ones of choice of the basic variables, and of historicity and irreversibility. The derivation of an on equilibrium grand-canonical statistical operator and a brief description of the all-important accompanying Nonlinear Quantum Kinetic Theory of relaxation processes are presented. The a spect of validation of the theory (comparison of theory and experiment) is reviewed in compact form, and its use is illustrated in a study of a nonequilibrium system of quantum oscillators embedded in a thermal bath and under the action of an external force, showing how a far-reaching generalization of Mori-Langev in equations arises.232752835305Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)