  Dynamical vertex approximation is a Feynman diagrammatic extension of
dynamical mean field theory, including non-local correlations on all time and
length scales. Starting with the Dyson and the parquet equations, the lecture
notes give an elementary introduction to the dynamical vertex approximation. As
a benchmark, results for an exactly solvable benzene Hubbard ring are
presented. Recent highlights, the calculation of the critical exponents of the
Hubbard model in 3D and that long-range antiferromagnetic correlations in 2D
actually shift the (paramagnetic) Mott transition to interaction U=0, are
reviewed.
