Integrable quantum field theories and integrable lattice models have been studied for several decades, but during the last few years new ideas have emerged that have considerably changed the topic. The first group of papers published here is concerned with integrable structures of quantum lattice models related to quantum group symmetries. The second group deals with the description of integrable structures in two-dimensional quantum field theories, especially boundary problems, thermodynamic Bethe ansatz and form factor problems. Finally, a major group of papers is concerned with the purely mathematical framework that underlies the physically-motivated research on quantum integrable models, including elliptic deformations of groups, representation theory of non-compact quantum groups, and quantization of moduli spaces.

Integrable quantum field theories and integrable lattice models have been studied for several decades, but during the last few years new ideas have emerged that have considerably changed the topic. The first group of papers published here is concerned with integrable structures of quantum lattice models related to quantum group symmetries. The second group deals with the description of integrable structures in two-dimensional quantum field theories, especially boundary problems, thermodynamic Bethe ansatz and form factor problems. Finally, a major group of papers is concerned with the purely mathematical framework that underlies the physically-motivated research on quantum integrable models, including elliptic deformations of groups, representation theory of non-compact quantum groups, and quantization of moduli spaces.

Ten years ago the Sunnner Institute on "Trends in Particle The- ory" was held in Bonn. Among other subj ects J. Wess spoke on his work wi th B. ZlDllino on "Fermi - Bose-Supersymmetry". In the meantime this subject has developed into one of the most exciting fields of research and the Bonn Summer Institute (August 20 - August 31 1984) was devoted exclusively to supersymmetry. The main aim of the Summer Institute was to provide a compre- hensive introduction for mainly young post-doctoral theoretical physicists to the currently most discussed subjects in supersynnne- try and supergravity. The intention was to emphasize the pedagogi- cal presentation. The seminars given in addition to the introduc- tory lectures treat more specialized subjects and are closer to research reports. Since the topics, ranging fromalgebraic structures to experimental implications do not arrange easily in a one-dimension- al array, the lectures are reproduced in alphabetic order of the lec- turers.The Summer Institute was made possible by the NATO Advanced Study Programme, additional support was granted by the Bundesmi- nisterium fur Forschung und Technologie and the Ministerium fur Wissenschaft und Forschung of Nordrhein-Westfalen. We gratefully acknowledge their cooperation. It is a pleasure to thank the lecturers and seminar speakers for the effort invested in the presentation of the lectures and in their collaboration in preparing the written notes.

Integrable quantum field theories and integrable lattice models have been studied for several decades, but during the last few years new ideas have emerged that have considerably changed the topic. The first group of papers published here is concerned with integrable structures of quantum lattice models related to quantum group symmetries. The second group deals with the description of integrable structures in two-dimensional quantum field theories, especially boundary problems, thermodynamic Bethe ansatz and form factor problems. Finally, a major group of papers is concerned with the purely mathematical framework that underlies the physically-motivated research on quantum integrable models, including elliptic deformations of groups, representation theory of non-compact quantum groups, and quantization of moduli spaces.

Integrable quantum field theories and integrable lattice models have been studied for several decades, but during the last few years new ideas have emerged that have considerably changed the topic. The first group of papers published here is concerned with integrable structures of quantum lattice models related to quantum group symmetries. The second group deals with the description of integrable structures in two-dimensional quantum field theories, especially boundary problems, thermodynamic Bethe ansatz and form factor problems. Finally, a major group of papers is concerned with the purely mathematical framework that underlies the physically-motivated research on quantum integrable models, including elliptic deformations of groups, representation theory of non-compact quantum groups, and quantization of moduli spaces.

Ten years ago the Sunnner Institute on "Trends in Particle The- ory" was held in Bonn. Among other subj ects J. Wess spoke on his work wi th B. ZlDllino on "Fermi - Bose-Supersymmetry". In the meantime this subject has developed into one of the most exciting fields of research and the Bonn Summer Institute (August 20 - August 31 1984) was devoted exclusively to supersymmetry. The main aim of the Summer Institute was to provide a compre- hensive introduction for mainly young post-doctoral theoretical physicists to the currently most discussed subjects in supersynnne- try and supergravity. The intention was to emphasize the pedagogi- cal presentation. The seminars given in addition to the introduc- tory lectures treat more specialized subjects and are closer to research reports. Since the topics, ranging fromalgebraic structures to experimental implications do not arrange easily in a one-dimension- al array, the lectures are reproduced in alphabetic order of the lec- turers.The Summer Institute was made possible by the NATO Advanced Study Programme, additional support was granted by the Bundesmi- nisterium fur Forschung und Technologie and the Ministerium fur Wissenschaft und Forschung of Nordrhein-Westfalen. We gratefully acknowledge their cooperation. It is a pleasure to thank the lecturers and seminar speakers for the effort invested in the presentation of the lectures and in their collaboration in preparing the written notes.