part, 1 Part I Knots, links, and invariant polynomials -- chapter 1 Introduction -- chapter 2 Reidemeister moves. Knot arithmetics -- chapter 3 Links in 2–surfaces in R3. Simplest link invariants -- chapter 4 Fundamental group. The knot group -- chapter 5 The knot quandle and the Conway algebra -- chapter 6 Kauffman’s approach to Jones polynomial -- chapter 7 Properties of Jones polynomials. Khovanov’s complex -- part, 2 Part II Theory of braids -- chapter 8 Braids, links and representations of braid groups -- chapter 9 Braids and links. Braid construction algorithms -- chapter 10 Algorithms of braid recognition -- chapter 11 Markov’s theorem. The Yang-Baxter equation -- part, 3 Part III Vassiliev’s invariants -- chapter 12 Definition and Basic notions of Vassiliev invariant theory -- chapter 13 The chord diagram algebra -- chapter 14 The Kontsevich integral and formulae for the Vassiliev invariants -- part, 4 Part IV Atoms and d–diagrams -- chapter 15 Atoms, height atoms and knots -- chapter 16 The bracket semigroup of knots -- part, 5 Part V Virtual knots -- chapter 17 Virtual knots. Basic definitions and motivation -- chapter 18 Invariant polynomials of virtual links -- chapter 19 Generalised Jones–Kauffman polynomial -- chapter 20 Long virtual knots and their invariants -- chapter 21 Virtual braids -- part, 6 Part VI Other theories -- chapter 22 3-manifolds and knots in 3-manifolds -- chapter 23 Legendrian knots and their invariants.