The algebraic supergroup $SL(m|n)$ is studied in detail, and the Hopf algebra structure of the algebra representing its functor of points is given explicitly. The quantization of the supergroup $SL(m|n)$, together with its coaction on suitable quantum spaces is presented following Manin's approach. Free download on line at: http://arxiv.org/PS_cache/math/pdf/0111/0111113v2.pdf