Geant4 simulation of annihilation and excitation of positronium

The purpose of this report is to document the work done during the summer of 2016 (18/6- 26/8) as a part of the CERN Summer Student Programme. The work has been done at the AEgIS (Antihydrogen Experiment: Gravity, Interferometry, Spectroscopy) collaboration under the supervision of Lillian Smestad and Michael Doser. The goal of the project was to create a Monte Carlo simulation in Geant4, of Positronium annihilation and excitation in the positron test chamber of the AEgIs experiment.