  We calculate the Kauffman bracket skein module (KBSM) of the complement of
all two-bridge links. For a two-bridge link, we show that the KBSM of its
complement is free over the ring $\BC[t^{\pm 1}]$ and when reducing $t=-1$, it
is isomorphic to the ring of regular functions on the character variety of the
link group.
