Advances in material quality and refinement of experimental methods over the past two decades have enabled researchers to reach a consensus on several aspects of the phase diagram of high-temperature superconducting cuprates. Theoretical methods have also developed considerably during this period. In this series of four lessons, I give an overview of experimental results and then focus on two classes of theoretical methods and what they tell us about the physics of high-temperature superconductors and other highly correlated materials, such as the organic layered superconductors of the BEDT family. I hope to convey the idea that we are beginning to reach a certain agreement between theory and experiment.
The lessons will last an hour and a half, but will generally be divided into two parts with a short break in between. The first part of each talk will be broadly accessible and the second - particularly for the last two lessons - will be a little more formal, developing some of the more specialized aspects of the corresponding first part.