One-Cocycles and Knot Invariants is about classical knots, i.e. smooth oriented knots in 3-space. It introduces discrete combinatorial analysis in knot theory in order to solve a global tetrahedron equation. This new technique is then used in order to construct combinatorial 1-cocycles in a certain moduli space of knot diagrams. The construction of the moduli space makes use of the meridian and of the longitude of the knot. The combinatorial 1-cocycles are then lifts of the well-known Conway polynomial of knots and they can be calculated in polynomial time. The 1-cocycles can distinguish...