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This volume presents the invited lectures of the workshop "Infinite Dimensional Algebras and Quantum Integrable Systems'' held in July 2003 at the University of Algarve, Faro, Portugal, as a satellite workshop of the XIV. International Congress on Mathematical Physics. Recent developments in the theory of infinite dimensional algebras and their applications to quantum integrable systems are reviewed by some of the leading experts in the field. The volume will be of interest to a broad audience from graduate students to researchers in mathematical physics and related fields. Contributors: E. Frenkel O.A. Castro-Alvaredo and A. Fring V.G. Kac and M. Wakimoto A. Gerasimov, S. Kharchev and D. Lebedev H.E. Boos, V.E. Korepin and F.A. Smirnov Kanehisa Takasaki Takashi Takebe L.A. Takhtajan and Lee-Peng Teo V. Tarasov.

Lie algebras --- Lie superalgebras --- Curves --- Functions of several complex variables --- Quantum theory --- Calculus --- Conic sections --- Geometry, Analytic --- Geometry, Differential --- Geometry, Enumerative --- Mathematics --- Shapes --- Superalgebras --- Algebra. --- Quantum theory. --- Mathematical physics. --- Topological Groups. --- Matrix theory. --- Systems theory. --- Quantum Physics. --- Mathematical Methods in Physics. --- Topological Groups, Lie Groups. --- Linear and Multilinear Algebras, Matrix Theory. --- Systems Theory, Control. --- System theory. --- Groups, Topological --- Continuous groups --- Physical mathematics --- Physics --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Mathematical analysis --- Systems, Theory of --- Systems science --- Science --- Philosophy --- Quantum physics. --- Physics. --- Topological groups. --- Lie groups. --- Groups, Lie --- Symmetric spaces --- Topological groups --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics