This is an easily accessible introduction to the subject that can be read as a first year graduate course or even earlier. It assumes very little knowledge of differentiable manifolds and functional analysis and includes coverage of recent developments. Particular emphasis is on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma). This textbook is suited for graduate students and undergraduate students in mathematics and theoretical physics.

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 Supérieure Paris, Max-Planck-Inst Bonn, University Essen, IHES Paris.

Professor: Cologne 1998-2002, Paris since 2002.