We describe a new, free and open source semi-analytic model of galaxy formation, G ALACTICUS. The G ALACTICUS model was designed to be highly modular to facilitate expansion and the exploration of alternative descriptions of key physical ingredients. We detail the G ALACTICUS engine for evolving galaxies through a merging hierarchy of dark matter halos and give details of the specific implementations of physics currently available in G ALACTICUS. Finally, we show results from an example model that is in reasonably good agreement with several observational datasets. We use this model to explore numerical convergence and to demonstrate the types of information which can be extracted from G ALACTICUS.