  A method to obtain explicit and complete topological solution of SU(2)
Chern-Simons theory on $S^3$ is developed. To this effect the necessary aspects
of the theory of coloured-oriented braids and duality properties of conformal
blocks for the correlators of $SU(2)_k$ Wess-Zumino conformal field theory are
presented. A large class of representations of the generators of the groupoid
of coloured-oriented braids are obtained. These provide a whole lot of new link
invariants of which Jones polynomials are the simplest examples. These new
invariants are explicitly calculated as illustrations for knots upto eight
crossings and two-component multicoloured links upto seven crossings.

High Energy Physics - Theory;Quantum Algebra