Conformal methods in general relativity Differential geometry Spacetime spinors Space spinors Conformal extensions of exact solutions Asymptotic simplicity The conformal Einstein field equations Matter models Asymptotics The conformal constraint equations Methods of the theory of hyperbolic differential equations Hyperbolic reductions Causality and the Cauchy problem in general relativity De Sitter like spacetimes Minkowski like spacetimes Anti de Sitter like spacetimes Characteristic problems for the conformal field equations Static solutions Spatial infinity Perspectives