The study of the correlated motion of electrons in solids is of increasing importance in condensed matter physics. In the past few years, the discovery of high-temperature superconductors has stimulated an enormous theoretical effort in this area, building on earlier theories of heavy-fermion and organic superconductors, and magnetic insulators. In a separate development the discovery of the fractional quantum Hall effect stimulated research into the behavior of the two-dimensional electron gas in a strong transverse magnetic field.The lectures at this school gave a systematic presentation of the current status of the theory in these areas. They covered the fractional quantum Hall effect and the many-body physics of the Hubbard model and its extensions, paying particular attention to the properties of doped insulators which are relevant for high-temperature superconductivity. There were detailed discussions of situations for which controlled calculations may be carried out — specifically infinite dimensions, one dimension, and generalized models in which the fermions have N components and N → •.Contents:Charge Fluctuation Models of Superconductivity (P B Littlewood)Investigation of Correlated Electron Systems Using the Limit of High Dimensions (D Vollhardt)The Large N Expansion in the Strong Correlation Problem (G Kotliar)The Semiclassical Expansion of the T-J Model (A Auerbach)The Many-Body Problem in One Dimension (V J Emery)Interacting Fermions in One Dimension: From Weak to Strong Correlation (H J Schulz)The Quantum Hall Effect: The Article (A Karlhede et al)Readership: Condensed matter, theoretical and experimental physicists.