  We develop a basic theory of affine group dg-schemes, their Lie algebraic
counterparts and linear representations. We prove Tannaka type reconstruction
theorems that an affine group dg-scheme can be recovered from the dg-tensor
category of its linear representations as well as from the rigid dg-tensor
category of its finite dimensional linear representations along with the
forgetful functors to the underlying dg-tensor category of cochain complexes.
