Based on the research of the hypergroup’structure of the free Abelian group with one Generator

this paper creates the theory of the hypergroup’s structure on the free Abelian group with two Generators

and gives deeply analyse and study. At the same time

this paper gives the homomorphism method from the free Abelian group of two Generators to the real number additive group. More over

this paper studies and classifies the structure of the hypergroup on free Abelian group.In this foundation

this paper makes the method how to classify the normal hypergroup.With strict proof

this paper has drawn an important conclusion that the free Abelian group is isomorphic to the real number additive group and its subgroup.