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Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma) Daniel Huybrechts is currently Professor of Mathematics at the University Denis Diderot in Paris. Brief career details: Studies of math at Humboldt University Berlin and Max-=Planck-Institute Bonn 1985-1992. Post-doctorial positions at Inst. for Advanced Study Priceton, Ecole Normale Suprieure Paris, Max-Planck-Inst Bonn, University Essen, IHES Paris. Professor: Cologne 1998-2002, Paris since 2002.

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