  The theoretical investigation of charge (and spin) transport at nanometer
length scales requires the use of advanced and powerful techniques able to deal
with the dynamical properties of the relevant physical systems, to explicitly
include out-of-equilibrium situations typical for electrical/heat transport as
well as to take into account interaction effects in a systematic way.
Equilibrium Green function techniques and their extension to non-equilibrium
situations via the Keldysh formalism build one of the pillars of current
state-of-the-art approaches to quantum transport which have been implemented in
both model Hamiltonian formulations and first-principle methodologies. We offer
a tutorial overview of the applications of Green functions to deal with some
fundamental aspects of charge transport at the nanoscale, mainly focusing on
applications to model Hamiltonian formulations.
