On the homology theory of fibre spaces

The $A(\text{inft})$-algebra structure in homology of a DG-algebra is constructed. This structure is unique up to isomorphism of $A(\mathrm{\infty })$ algebras. Connection of this structure with Massey products is indicated. The notion of $A(\mathrm{\infty })$-module over an $A(\mathrm{\infty })$-algebra is introduced and such a structure is constructed in homology of a DG-modules over a DG-algebra. The theory of twisted tensor products is generalized from the case of DG-algebras to the case of $A(\mathrm{\infty })$-algebras. These algebraic results are used to describe homology of classifying spaces, cohomology of loop spaces, and homology of fibre bundles.