The GW approximation is an approximation within many body perturbation theory that takes certain diagrammatic contributions into account in the screened Coulomb interaction. The self-energy is approximated to be G (the Greens function) times the screened Coulomb interaction W. The GW method provides access to the spectral properties of the system by means of determining the energies of the so-called quasi-particles and it is currently one of the most accurate many-body methods to calculate band-gaps.
For lectures, check here:
- GW approximation by Merzuk Kaltak
Also check out the GW category on the VASP Wiki for a detailed overview of GW algorithms implemented in VASP.