  For transcendental values of q the quantum tangent spaces of all
left-covariant first order differential calculi of dimension less than four on
the quantum group $\SLq 2$ are given. All such differential calculi $\Gamma $
are determined and investigated for which the left-invariant differential
one-forms $\omega (u^1_2)$, $\omega (u^2_1)$ and $\omega (u^1_1-u^2_2)$
generate $\Gamma $ as a bimodule and the universal higher order differential
calculus has the same dimension as in the classical case. Important properties
(cohomology spaces, *-structures, braidings, generalized Lie brackets) of these
calculi are examined as well.
  Keywords: quantum groups, noncommutative differential calculus, quantum
tangent space
