Strongly Correlated Magnetic and Superconducting Systems : Proceedings of the El Escorial Summer School Held in Madrid Spain 15 19 July 1996 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