  We classify all 4-dimensional first order bicovariant calculi on the
Jordanian quantum group GL_{h,g}(2) and all 3-dimensional first order
bicovariant calculi on the Jordanian quantum group SL_{h}(2). In both cases we
assume that the bicovariant bimodules are generated as left modules by the
differentials of the quantum group generators. It is found that there are 3
1-parameter families of 4-dimensional bicovariant first order calculi on
GL_{h,g}(2) and that there is a single, unique, 3-dimensional bicovariant
calculus on SL_{h}(2). This 3-dimensional calculus may be obtained through a
classical-like reduction from any one of the three families of 4-dimensional
calculi on GL_{h,g}(2). Details of the higher order calculi and also the
quantum Lie algebras are presented for all calculi. The quantum Lie algebra
obtained from the bicovariant calculus on SL_{h}(2) is shown to be isomorphic
to the quantum Lie algebra we obtain as an ad-submodule within the Jordanian
universal enveloping algebra U_{h}(sl(2)) and also through a consideration of
the decomposition of the tensor product of two copies of the deformed adjoint
module. We also obtain the quantum Killing form for this quantum Lie algebra.
