$D_\infty$-differential $E_\infty$-algebras and spectral sequences of fibrations

The notion of an $E_\infty$-algebra with a filtration is introduced. The connections are established between $E_\infty$-algebras with filtrations and the theory of $D_\infty$-differential $E_\infty$-algebras over fields. Based on the technique of $D_\infty$-differential $E_\infty$-algebras, the apparatus of spectral sequences is developed for $E_\infty$-algebras with filtrations, and applications of this apparatus to the multiplicative cohomology spectral sequences of fibrations are given.
Bibliography: 21 titles.