This volume is targeted at theoretical physicists, mathematical physicists and mathematicians working on mathematical models for physical systems based on symmetry methods and in the field of Lie theory understood in the widest sense. It includes contributions on Lie theory, with two papers by the famous mathematician Kac (one paper with Bakalov), further papers by Aoki, Moens. Some other important contributions are in: field theory - Todorov, Grosse, Kreimer, Sokatchev, Gomez; string theory - Minwalla, Staudacher, Kostov; integrable systems - Belavin, Helminck, Ragoucy; quantum-mechanical and probabilistic systems - Goldin, Van der Jeugt, Leandre; quantum groups and related objects - Jakobsen, Arnaudon, Andruskiewitsch; and others.