Structure of Ann-Categories

This paper presents the structure conversion by which from an Ann-category $A,$ we can obtain its reduced Ann-category of the type $(R,M)$ whose structure is a family of five functions $k=(xi,eta,alpha,lambda,rho)$. Then we will show that each Ann-category is determined by three invariants: 1. The ring $Pi_0(A)$ of the isomorphic classes of objects of $A$, 2. $Pi_0(A)$-bimodule $Pi_1(A) = Aut_{A}(0),$ 3. The element $ bar{k}in H^{3}_{M}(Pi_0(A), Pi_1(A))$ (the ring cohomology due to MacLane).