th This volume contains the proceedings of the X Congress of the Interna­ tional Association of Mathematical Physics, held at the University of Leipzig from 30 July until 9 August 1991. There were more than 400 participants, from 29 countries, making it a truly international gathering. The congress had the support of the Deutsche Forschungsgemeinschaft, the European Economic Community, the International Association of Math­ ematical Physics, the International Mathematical Union and the Interna­ tional Union of Pure and Applied Physics. There were also sponsors from in­ dustry and commerce: ATC Mann, Deutsche Bank AG, Miele & Cie GmbH, NEC Deutschland GmbH, Rank Xerox, Siemens AG and