Introduction -- States, trails, and the clock theorem -- State polynomials and the duality conjecture -- Knots and links -- Axiomatic link calculations -- Curliness and the Alexander polynomial -- The coat of many colors -- Spanning surfaces -- The genus of alternative links -- Ribbons knots and the Arf invariant -- Appendix: The classical Alexander polynomial -- References -- Supplement: Remarks on formal knot theory -- Appendix: New invariants in the theory of knots.
