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For an understanding of the SYZ conjecture it is necessary to understand the framework of D-branes. I believe that a very good introduction, still unmatched in its comprehensiveness, is the book by Hori et al. on "Mirror Symmetry". This book has been made freely available by the Clay Math Institute and can be downloaded from their website http://www.claymath.org/library/monographs/cmim01.pdf. A more recent reference is the book by Joyce on "Riemannian Holonomy Groups and Calibrated Geometry", which contains a discussion of the SYZ conjecture from a more rigorous point of view.

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For an understanding of the SYZ conjecture it is necessary to understand the framework of D-branes. I believe that a very good introduction, still unmatched in its comprehensiveness, is the book by Hori et al. on "Mirror Symmetry". This book has been made freely available by the Clay Math Institute and can be downloaded from their website http://www.claymath.org/library/monographs/cmim01.pdf.