This volume contains the proceedings of the Fourth Taniguchi International Symposium on the Theory of Condensed Matter, which was held at Senkari Semi­ nar House of Kwansei Gakuin Universi~y in Sanda-shi, Japan, during the period of 3-8 November 1981. The topic of the symposium was "Anderson rocalization," one of the most fundamental problems in condensed-matter physics. Since Anderson's classic paper was published in 1958, much theoretical and experimental effort has been performed to study the problem of electron localization in a random potential. Quite recently, Abrahams, Anderson, Licciardello, and Ramakrishnan proposed a scaling theory of the Anderson lo­ calization which made it possible to perform microscopic investigations. Rapid progress has followed and we are now getting a coherent picture of the behavior of electrons in disordered systems. When we organized the symposium, we asked Dr. Anderson to participate in it and to give a review talk on theoretical aspects of the problem. Though he kindly accepted our invitation, he could not come due to a sudden illness. A review talk was given by Professor Thouless who kindly accepted our request to take the place of Dr. Anderson. Fortunately, Dr. Anderson has since re­ covered from his illness.

I. Anderson Localization.- Survey of Localization: Are Noninteracting Electrons Fully Understood?.- The Anderson Transition and the Nonlinear ?-Model.- Anderson Localization in Nonlinear ? Model Representation.- Self-Consistent Diagrammatic Theory of Anderson Localization.- Self-Consistent Treatment of Two-Dimensional Anderson Localization in the Absence of Time Reversal Symmetry.- Localization in One-Dimensional and Quasi-One-Dimensional System.- Numerical Studies of Localization in Two Dimensions.- Numerical Study of DC Conductivity in Two-Dimensional Disordered Systems.- Interaction Effects in Disordered Systems.- Interaction Effects in Two-Dimensional Disordered Systems.- Localization Versus Superconductivity.- Kondo Effects and Localization in Two Dimensions.- Application of the Recent Theory of Anderson Localization to Doped Semiconductors.- Dielectric and Optical Anomalies Near the Anderson Metal-Insulator Transition.- Localization in n-InSb.- Interplay of Disorder and Coulomb Interactions in Anderson-Localized States.- Extended Effective Medium Theory for Conductivity.- II. Quantized Hall Effect.- Hall Effect and Electron Localization in a Two-Dimensional System in Strong Magnetic Fields.- Localization in a Strong Magnetic Field.- The Quantized Hall Effect and Other Macroscopic Quantum Phenomena.- A Calculation of Two-Dimensional Hall Conductivity Under Strong Magnetic Fields - Wigner Representation.- III. Spin Class.- Breaking of Ergodicity in Disordered Systems: The Case of Spin Glasses.- Index of Contributors.