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This volume discusses mirror symmetry of Calabi-Yau manifolds, quantum algebra, algebraic geometry and integrable systems. The contributors include V Batyrev, R Donagi, B Dubrovin, E Getzler, A Givental, M Gross, M Kapranov, T Kawai, M Kobayashi, T Maeno, Y Namikawa, K Ueno, M-H Saito and Y Shimizu.