  By direct calculations of matrix form of super Jacobi and mixed super Jacobi
identities which are obtained from adjoint representation, and using the
automorphism supergroup of the gl(1|1) Lie superalgebra, we determine and
classify all gl(1|1) Lie superbialgebras. Then, by calculating their classical
r-matrices, the gl(1j1) coboundary Lie superbialgebras and their types
(triangular, quasi-triangular or factorizable) are determined, furthermore in
this way super Poisson structures on the GL(1|1) Lie supergroup are obtained.
Also, we classify Drinfeld superdoubles based on the gl(1|1) as a theorem.
Afterwards, as a physical application of the coboundary Lie superbialgebras, we
construct a new integrable system on the homogeneous superspace OSp(1|2)/U(1).
Finally, we make use of the Lyakhovsky and Mudrov formalism in order to build
up the deformed gl(1|1) Lie superalgebra related to all gl(1|1) coboundary Lie
superbialgebras. For one case, the quantization at the supergroup level is also
provided, including its quantum R-matrix.
