  We address one of the open problems in quantization theory recently listed by
Rieffel. By developping in detail Connes' tangent groupoid principle and using
previous work by Landsman, we show how to construct a strict, flabby
quantization, which is moreover an asymptotic morphism and satisfies the
reality and traciality constraints, on any oriented Riemannian manifold. That
construction generalizes the standard Moyal rule. The paper can be considered
as an introduction to quantization theory from Connes' point of view.
