We review recent developments in special geometry and explain its role in the
theory of supersymmetric black holes. To make this article self-contained, a
short introduction to black holes is given, with emphasis on the laws of black
hole mechanics and black hole entropy. We also summarize the existing results
on the para-complex version of special geometry, which occurs in Euclidean
supersymmetry. The role of real coordinates in special geometry is illustrated,
and we briefly indicate how Euclidean supersymmetry can be used to study
stationary black hole solutions via dimensional reduction over time.
This article is an updated and substantially extended version of the previous
review article `New developments in special geometry', hep-th/0602171.Comment: 39 pages, Contribution to the Handbook on Pseudo-Riemannian Geometry
and Supersymmtry, ed. V. Corte
