  Berwald metrics are particular Finsler metrics which still have linear
Berwald connections. Their complete classification is established in an earlier
work, [Sz1], of this author. The main tools in these classification are the
Simons-Berger holonomy theorem and the Weyl-group theory. It turnes out that
any Berwald metric is a perturbed-Cartesian product of Riemannian, Minkowski,
and such non-Riemannian metrics which can be constructed on irreducible
symmetric manifolds of $rank > 1$. The existence of these metrics are well
established by the above theories.
  The present paper has several new features. First, the Finsler functions of
Berwald manifolds are explicitly described by the Chevalley polynomials. New
results are also the complete lists of reversible (d(x,y)=d(y,x)) resp.
irreversible ($d(x,y)\not =d(y,x)$) Berwald metrics. The Cartan symmetric
Finsler manifolds are also completely determined. The paper is concluded by
proving that a Berwald metric is uniquely determined by the Minkowski metric
induced on an arbitrarily fixed maximal totalgeodesic flat submanifold (Cartan
flat). Moreover, any two Cartan flats are isometric.
