  Various aspects of the Cauchy problem for the Einstein equations are
surveyed, with the emphasis on local solutions of the evolution equations.
Particular attention is payed to giving a clear explanation of conceptual
issues which arise in this context. The question of producing reduced systems
of equations which are hyperbolic is examined in detail and some new results on
that subject are presented. Relevant background from the theory of partial
differential equations is also explained at some length
