  An attempt is made of giving a self-contained (although incomplete)
introduction to holomorphic ideas in general relativity, following work over
the last thirty years by several authors. The main topics are complex
manifolds, two-component spinor calculus, conformal gravity, alpha-planes in
Minkowski space-time, alpha-surfaces and twistor geometry, anti-self-dual
space-times and Penrose transform, spin-3/2 potentials, heaven spaces and
heavenly equations.
