Cosmology with the Cosmic Microwave Background

Cosmology is the focal point of modern physics, with the interplay of mathematics, physics and astronomy. It allows for extreme speculation but also requires stringent predictions to be compared to precise experimental facts. The cosmic microwave background, the relic radiation left over from the early universe supplies us with a clean observable, which can link physical processes when the universe was a fraction of its age, to high precision, high resolution observations. In these lectures I will develop the physics of the cosmic microwave background, describe the mathematical tools one must use to make accurate predictions and the statistical tools necessary to compare it to data. I will discuss what we currently know about the state of the universe from the existing data.