  This tutorial article presents a "bottom-up" view of electrical resistance
starting from something really small, like a molecule, and then discussing the
issues that arises as we move to bigger conductors. Remarkably, no serious
quantum mechanics is needed to understand electrical conduction through
something really small, except for unusual things like the Kondo effect that
are seen only for a special range of parameters. This article starts with
energy level diagrams (section 2), shows that the broadening that accompanies
coupling limits the conductance to a maximum of q^2/h per level (sections 3,
4), describes how a change in the shape of the self-consistent potential
profile can turn a symmetric current-voltage characteristic into a rectifying
one (sections 5, 6), shows that many interesting effects in molecular
electronics can be understood in terms of a simple model (section 7),
introduces the non-equilibrium Green function (NEGF) formalism as a
sophisticated version of this simple model with ordinary numbers replaced by
appropriate matrices (section 8) and ends with a personal view of unsolved
problems in the field of nanoscale electron transport (section 9). Appendix A
discusses the Coulomb blockade regime of transport, while appendix B presents a
formal derivation of the NEGF equations. MATLAB codes for numerical examples
are listed in the appendix C.
