  We discuss quantum deformation of the affine transformation group and its Lie
algebra. It is shown that the quantum algebra has a non-cocommutative Hopf
algebra structure, simple realizations and quantum tensor operators. The
deformation of the group is achieved by using the adjoint representation. The
elements of quantum matrix form a Hopf algebra. Furthermore, we construct a
differential calculus which is covariant with respect to the action of the
quantum matrix.
