  In the presence of a variable magnetic field, the Weyl pseudodifferential
calculus must be modified. The usual modification, based on ``the minimal
coupling principle'' at the level of the classical symbols, does not lead to
gauge invariant formulae if the magnetic field is not constant. We present a
gauge covariant quantization, relying on the magnetic canonical commutation
relations. The underlying symbolic calculus is a deformation, defined in terms
of the magnetic flux through triangles, of the classical Moyal product.
