This volume, intended as a contribution to the 10th birthday of high Tc-superconductivity, conveys the essential ideas of the field and addresses researchers as well as graduate students. A special feature is the pedagogical treatment of a variety of modern computational methods to deal with non-pertubative effects in strongly correlated systems. Among the topics treated are the Hubbard models, real space renormalization group methods, quantum phase transitions, the non-linear sigma model, spin ladders and layers, and the quantum Hall effect.