preface part i. riemannian holonomy groups and calibrated geometry dominic joyce 1 introduction 2 introduction to holonomy groups 3 berger's classification of holonomy groups 4 kahler geometry and holonomy 5 the calabi conjecture 6 the exceptional holonomy groups 7 introduction to calibrated geometry 8 calibrated submanifolds in rn 9 constructions of sl m-folds in ctm 10 compact calibrated submanifolds 11 singularities of special lagrangian m-folds 12 the syz conjecture, and sl fibrations part ii. calabi-yau manifolds and mirror symmetry mark gross 13 introduction 14 the classical geometry of calabi-yau manifolds .15 kahler moduli and gromov-witten invariants 16 variation and degeneration of hodge structures 17 a mirror conjecture 18 mirror symmetry in practice 19 the strominger-yau-zaslow approach to mirror symmetry part iii. compact hyperkaihler manifolds daniel huybrechts 20 introduction 21 holomorphic symplectlc manifolds 22 deformations of complex structures 23 the beauville-bogomolov form 24 cohomology of compact hyperkahler manifolds 25 twistor space and moduli space 26 projectivity of hyperkahler manifolds 27 birational hyperkahler manifolds 28 the (birational) kahler cone references index