  For any n>1 we define an isotopy invariant, <Gamma>_n, for a certain set of
n-valent ribbon graphs Gamma in R^3, including all framed oriented links. We
show that our bracket coincides with the Kauffman bracket for n=2 and with the
Kuperberg's bracket for n=3. Furthermore, we prove that for any n, our bracket
of a link L is equal, up to normalization, to the SU_n-quantum invariant of L.
We show a number of properties of our bracket extending those of the Kauffman's
and Kuperberg's brackets, and we relate it to the bracket of
Murakami-Ohtsuki-Yamada. Finally, on the basis of the skein relations satisfied
by <.>_n, we define the SU_n-skein module of any 3-manifold M and we prove that
it determines the SL_n-character variety of pi_1(M).
