Construction of initial data for 3+1 numerical relativity

This lecture is devoted to the problem of computing initial data for the Cauchy problem of 3+1 general relativity. The main task is to solve the constraint equations. The conformal technique, introduced by Lichnerowicz and enhanced by York, is presented. Two standard methods, the conformal transversetraceless one and the conformal thin sandwich, are discussed and illustrated by some simple examples. Finally a short review regarding initial data for binary systems (black holes and neutron stars) is given. Submitted to: Journal of Physics: Conference Series, for the Proceedings of the VII Mexican School on Gravitation and Mathematical Physics, held in Playa del Carmen, Quintana Roo, Mexico (November 26 December 2, 2006)