Enumerative geometry and knot invariants

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We review the string/gauge theory duality relating Chern-Simons theory and topological strings on noncompact Calabi-Yau manifolds, as well as its mathematical implications for knot invariants and enumerative geometry.
69 pages, 13 figures, LaTeX, reference added, typos corrected. To appear in the Proceedings of the meeting of theoretical physicists and mathematicians held at Strasbourg, May 2002

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