  This paper develops a duality theory for connected cochain DG algebras, with
particular emphasis on the non-commutative aspects.
  One of the main items is a dualizing DG module which induces a duality
between the derived categories of DG left-modules and DG right-modules with
finitely generated cohomology.
  As an application, it is proved that if the canonical module $A / A^{\geq 1}$
has a semi-free resolution where the cohomological degree of the generators is
bounded above, then the same is true for each DG module with finitely generated
cohomology.
