  This tutorial outlines the basic theoretical concepts and tools which
underpin the fundamentals of phase-coherent electron transport through single
molecules. The key quantity of interest is the transmission coefficient T(E),
which yields the electrical conductance, current-voltage relations, the
thermopower S and the thermoelectric figure of merit ZT of single-molecule
devices. Since T(E) is strongly affected by quantum interference (QI), three
manifestations of QI in single-molecules are discussed, namely Mach-Zehnder
interferometry, Breit-Wigner resonances and Fano resonances. A simple MATLAB
code is provided, which allows the novice reader to explore QI in
multi-branched structures described by a tight-binding (Huckel) Hamiltonian.
More generally, the strengths and limitations of materials-specific transport
modelling based on density functional theory are discussed.
