Summary: [For the entire collection see Zbl 0716.00010.]
We present a general theory for the construction of link polynomials, topological invariants for knots and links, from an exactly solvable model satisfying the Yang-Baxter relation. First, we present a method to make a braid group representation from the Yang-Baxter operator, the constituent of the diagonal-to-diagonal transfer matrix, for the model at criticality. Second, we construct the Markov trace whose existence is a consequence of the crossing symmetry or the second inversion relation satisfied by the solvable model. Third, the general theory is applied to various models, by which a list of new link polynomials are constructed. Lastly, some extensions of the theory are presented. We conclude that a new and powerful approach to knot theory based on the theory of exactly solvable models has been established.