Understanding the formation of galaxies, the nature of dark matter, and the symbiotic relationship between supermassive black holes, energy feedback, and the pollution of the Cosmic Web, are the Key Questions facing cosmology in the 21st century. We have established the Commonwealth Cosmology Initiative (CCI) to provide a platform for Australia's nascent High Performance Computational (HPC) and Theoretical Astrophysics communities to compete internationally in these disciplines. The CCI will develop a suite of HPC and phenomenological simulations suitable for understanding the formation of galaxies, their interaction with the Cosmic Web, and the structure of dark matter halos.