Gaudin Model and Opers -- Integrable Models with Unstable Particles -- Quantum Reduction in the Twisted Case -- Representation Theory and Quantum Integrability -- Connecting Lattice and Relativistic Models via Conformal Field Theory -- Elliptic Spectral Parameter and Infinite-Dimensional Grassmann Variety -- Trigonometric Degeneration and Orbifold Wess-Zumino-Witten Model. II -- Weil-Petersson Geometry of the Universal Teichmüller Space -- Duality for Knizhinik-Zamolodchikov and Dynamical Equations, and Hypergeometric Integrals.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.