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 Advanced Studies in Pure Mathematics 2008; 510 pp; hardcover Volume: 51 ISBN-10: 4-931469-46-9 ISBN-13: 978-4-931469-46-4 List Price: US$76 Member Price: US$60.80 Order Code: ASPM/51 The articles in this volume provide a panoramic view of the role of geometry in integrable systems, firmly rooted in surface theory but currently branching out in all directions. The longer articles by Bobenko (the Bonnet problem), Dorfmeister (the generalized Weierstrass representation), Joyce (special Lagrangian 3-folds) and Terng (geometry of soliton equations) are substantial surveys of several aspects of the subject. The shorter ones indicate more briefly how the classical ideas have spread throughout differential geometry, symplectic geometry, algebraic geometry, and theoretical physics. Volumes in this series are freely available electronically 5 years post-publication. Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS. Readership Graduate students and research mathematicians interested in mathematical physics. Table of Contents A. I. Bobenko -- Exploring surfaces through methods from the theory of integrable systems: The Bonnet problem J. Dorfmeister -- Generalized Weierstraß representations of surfaces A. Fujioka and J. Inoguchi -- Timelike surfaces with harmonic inverse mean curvature C. Gu -- Darboux transformations and generalized self-dual Yang-Mills flows F. Hélein and P. Romon -- From CMC surfaces to Hamiltonian stationary Lagrangian surfaces D. Joyce -- Special Lagrangian 3-folds and integrable systems X. Liu -- Quantum product, topological recursion relations, and the Virasoro conjecture S. Matsutani -- A generalized Weierstrass representation for a submanifold $$S$$ in $$\mathbb{E}^n$$ arising from the submanifold Dirac operator I. McIntosh -- Harmonic tori and their spectral data R. Miyaoka -- Isoparametric geometry and related fields H. Pedersen -- Kähler Ricci solitons W. Rossman, M. Umehara, and K. Yamada -- Period problems for mean curvature one surfaces in $$H^3$$ (with applications to surfaces of low total curvature) C.-L. Terng -- Geometries and symmetries of soliton equations and integrable elliptic equations P. Topalov -- A-integrability of geodesic flows and geodesic equivalence