  We develop a general theory of algebraic group superschemes, which are not
necessarily affine. Our key result is a category equivalence between those
group superschemes and Harish-Chandra pairs, which generalizes the result known
for affine algebraic group superschemes. Then we present the applications,
including the Barsotti-Chevalley Theorem in the super context, and an explicit
construction of the quotient superscheme $\mathbb{G}/\mathbb{H}$ of an
algebraic group superscheme $\mathbb{G}$ by a group super-subscheme
$\mathbb{H}$.
