The aim of this book is to present a formulation of the non-equilibrium physics in nanoscale systems in terms of many-body states and operators and, in addition, discuss a diagrammatic approach to Green functions expressed by many-body states. The intention is not to give an account of strongly correlated systems as such. Thus, the focus of this book ensues from the typical questions that arise when addressing nanoscale systems from a practical point of view, e.g. current-voltage asymmetries, negative differential conductance, spin-dependent tunneling. The focus is on nanoscale systems constituted of complexes of subsystems interacting with one another, under non-equilibrium conditions, in which the local properties of the subsystems are preferably being described in terms of its (many-body) eigenstates.