  The Jones polynomial and the Kauffman bracket are constructed, and their
relation with knot and link theory is described. The quantum groups and tangle
functor formalisms for understanding these invariants and their descendents are
given. The quantum group $U_q(sl_2)$, which gives rise to the Jones polynomial,
is constructed explicitly. The $3$-manifold invariants and the axiomatic
topological quantum field theories which arise from these link invariants at
certain values of the parameter are constructed.
