Cosmology studies the history and the structure of the universe. Observations show the ho- mogeneity and isotropy of the universe on large scales. For the homogenous and isotropic spacetimes, the equations of general relativity reduce to two ordinary di erential equations. These cosmological equations govern the evolution of the universe. We study these equations in detail, and show how observations are a ected by the expansion and curvature of the universe. The course covers the astronomical methods used to determine the expansion rate (i.e., the Hubble constant) and the mass density of the universe. Physical processes in the early universe such as nucleosynthesis, the formation of the microwave background, and galaxy formation will also be studied. The course begins with a concise introduction to the di erential-geometric methods and ends with advanced topics including in ation and cosmological perturbations. A good working knowledge of General Relativity is essential for many parts of this course.