  We study the scheme of formal arcs on a singular algebraic variety and its
images under truncations. We prove a rationality result for the Poincare series
of these images which is an analogue of the rationality of the Poincare series
associated to p-adic points on a p-adic variety. The main tools which are used
are semi-algebraic geometry in spaces of power series and motivic integration
(a notion introduced by M. Kontsevich). In particular we develop the theory of
motivic integration for semi-algebraic sets of formal arcs on singular
algebraic varieties, we prove a change of variable formula for birational
morphisms and we prove a geometric analogue of a result of Oesterle.
