TASI LECTURES ON COMPACTIFICATION AND DUALITY

We describe the moduli spaces of theories with 32 or 16 supercharges, from several points of view. Included is a review of backgrounds with D-branes (including type I ′ vacua and F-theory), a discussion of ho-lonomy of Riemannian metrics, and an introduction to the relevant portions of algebraic geometry. The case of K3 surfaces is treated in some detail.

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