  We show that the bicovariant first order differential calculi on a
factorisable semisimple quantum group are in 1-1 correspondence with
irreducible representations $V$ of the quantum group enveloping algebra. The
corresponding calculus is constructed and has dimension $dim V^2$. The
differential calculi on a finite group algebra $C G$ are also classified and
shown to be in correspondence with pairs consisting of an irreducible
representation $V$ and a continuous parameter in $C P^{dim V -1}$. They have
dimension $dim V$. For a classical Lie group we obtain an infinite family of
non-standard calculi. General constructions for bicovariant calculi and their
quantum tangent spaces are also obtained.
