  In this paper, twisted tensor product of DG algebras is studied and
sufficient conditions for smoothness of such a product are given. It is shown
that in the case of finite-dimensional DG algebras, applying this operation
offers great possibilities for constructing new examples of smooth DG algebras
and algebras. In particular, examples are given of families of algebras of
finite global dimension with two simple modules that have nontrivial moduli
spaces.
