This course is an account of modern cosmology. It will include a discussion on the large scale homogenous and isotropic nature of the Universe and how the Universe is expanding with time. This will be followed by a brief review of the aspects of General Relativity that we will need in the course. After that, we will discuss the constituents of the Universe and how the expansion of the Universe has changed over time. The apparent accelerating expansion of the Universe and the proposed dark energy explanation for it will also be discussed. The evidence for dark matter and what properties it appears to have will be reviewed. We will use the Boltzmann equation to understand big bang nuclear synthesis and the cosmic microwave background. These are two of the main observational pillars of the big bang model of the Universe. The Boltzmann equation will be used to study a thermal relic model of dark matter. We will then go on to study the inhomogeneity of large scale structure such as galaxies, galaxy clusters and the cosmic web. The anisotropies in the cosmic microwave background will be analysed. We will see how observations of both of these phenomena can allow us to tightly constrain many properties of the Universe. Pre-requisites - additional info: Prior astronomy courses would be useful but are not essential as we will cover any needed subjects during the course.