  The Moyal--Weyl description of quantum mechanics provides a comprehensive
phase space representation of dynamics. The Weyl symbol image of the Heisenberg
picture evolution operator is regular in $\hbar$. Its semiclassical expansion
`coefficients,' acting on symbols that represent observables, are simple,
globally defined differential operators constructed in terms of the classical
flow. Two methods of constructing this expansion are discussed. The first
introduces a cluster-graph expansion for the symbol of an exponentiated
operator, which extends Groenewold's formula for the Weyl product of symbols.
This Poisson bracket based cluster expansion determines the Jacobi equations
for the semiclassical expansion of `quantum trajectories.' Their Green function
solutions construct the regular $\hbar\downarrow0$ asymptotic series for the
Heisenberg--Weyl evolution map. The second method directly substitutes such a
series into the Moyal equation of motion and determines the $\hbar$
coefficients recursively. The Heisenberg--Weyl description of evolution
involves no essential singularity in $\hbar$, no Hamilton--Jacobi equation to
solve for the action, and no multiple trajectories, caustics or Maslov indices.
