  By associating a `motivic integral' to every complex projective variety X
with at worst canonical, Gorenstein singularities, Kontsevich proved that, when
there exists a crepant resolution of singularities Y of X, the Hodge numbers of
Y do not depend upon the choice of the resolution. In this article we provide
an elementary introduction to the theory of motivic integration, leading to a
proof of the result described above. We calculate the motivic integral of
several quotient singularities and discuss these calculations in the context of
the cohomological McKay correspondence.
