$D_\infty$-differential $A_\infty$-algebras and spectral sequences

In the present paper the construction of a $D_\infty$-differential $A_\infty$-(co)algebra is introduced and basic homotopy properties of this construction are studied. The connection between $D_\infty$-differential $A_\infty$-(co)algebras and spectral sequences is established, which enables us to construct the structure of an $A_\infty$ -coalgebra on the Milnor coalgebra directly from the differentials of the Adams spectral sequence.