Affine Vertex Operator Algebra

In this paper,A concrete construction of Affine vertex operator algebra V?k,0?is given.By using the properties of integrable highest weight module over Kac-Moody algebras,a description of unique maximal submodule I?k,0?is given and the Zhu's algebra of simple affine vertex operator algebra L?k,0?= V?k,0?/I?k,0?is calculated.For simple vertex operator algebra L?k,0?,by using Zhu's A?V?theory,we give a classification of its irreducible modules when level k is positive integer.Finally,the rationality and C2-cofinite properties of L?k,0?are also given.Finally,we give another approach to the classification by using the vertex representation of s???₂.