A quantitative understanding of bonding in condensed matter systems demands a solution of the many electron problem. This course will show how the many electron problem can be mapped onto single electron problems in an approximate way (Hartree and Hartree Fock approximations) and a formally exact way (density functional theory and the Kohn Sham equations). Further, some of the methodology used to solve the Kohn Sham equations in complex systems will be described. In the last part of the lectures, some examples will be analysed, and we will critically evaluate the strength and weaknesses of DFT and other ab-initio electronic structure methods.

**Niels** is a professor of theoretical physics at the University of Manchester. His research interests are in the theory of and computational approaches to Nuclear Physics, as well as the adjacent areas of Particle and Condensed Matter Physics. As well as this research, he contributes to Open Educational Resources and e-learning resources using simulations in Java and Mathematica.