  When travelling from the number fields theory to the function fields theory,
one cannot miss the deep analogy between rank 1 Drinfeld modules and the group
of root of unity and the analogy between rank 2 Drinfeld modules and elliptic
curves. But so far, there is no known structure in number fields theory that is
analogous to the Drinfeld modules of higher rank r > 2. In this paper we
investigate the classes of those Drinfeld modules of higher rank r > 2. We
describe explicitly the Weil polynomials defining the isogeny classes of rank r
Drinfeld modules for any rank r > 2. our explicit description of the Weil
polynomials depends heavily on Yu's classification of isogeny classes (analogue
of Honda-Tate at abelian varieties). Actually Yu has also explicitly did that
work for r = 2. To complete the classification, we define the new notion of
fine isomorphy invariants for any rank r Drinfeld module and we prove that the
fine isomorphy invariants together with J-invariants completely determine the
L-isomorphism classes of rank r Drinfeld modules defined over the finite field
L.

Number Theory