within the framework of jaynes predictive statistical mechanics, this book presents a detailed derivation of an ensemble formalism for open systems arbitrarily away from equilibrium. this involves a large systematization and extension of the fundamental works and ideas of the outstanding pioneers gibbs and boltzmann, and of bogoliubov, kirkwood, green, mori, zwanzig, prigogine and zubarev, among others. chapters 1 to 5 include a description of the philosophy, foundations, and construction (methodology) of the formalism, including the derivation of a nonequilibrium grand-canonical ensemble for far-from-equilibrium systems as well as the derivation of a quantum nonlinear kinetic theory and a response function theory together with a theory of scattering. in chapter 6 applications of the theory are cataloged, making comparisons with experimental data (a basic step for the validation of any theory). chapter 7 is devoted to the description of irreversible thermodynamics, providing a far-reaching generalization of informational-statistical thermodynamics. the last chapter gives an overall picture of the formalism, and questions and criticisms related to it are discussed. audience: this book is directed at an audience of researchers in the field of statistical mechanics and thermodynamics of open nonequilibrium systems. in addition, it is relevant for the study of far-from-equilibrium processes in condensed matter, particularly semiconductor physics, as well as molecular hydrodynamics, rheology, many-body systems with complex behavior and areas of engineering, etc. the book can also be used as a complement to advanced graduate courses in statistical mechanics.