Cargèse Lectures on Black Holes, Dyons, and Modular Forms

For several N=4 supersymmetric compactifications, it is now possible to count the dyonic states exactly and compare their degeneracies with the entropy of the corresponding black holes. The dyon partition function is given in terms of a Siegel modular form. For large charges, the logarithm of the degeneracy determined from the partition function is in striking agreement with the Wald entropy of corresponding black holes including subleading corrections. These lectures review this recent progress and discuss a number of puzzles in the physical interpretation of the dyon partition function and their resolution.