“This text is a comprehensive and well written introduction to quantum and Vassiliev invariants of knots. … There is sufficient detail for students and exercises. The text is also an excellent reference for researchers interested in quantum and Vassiliev invariants.” (Heather A. Dye, zbMATH 1425.57007, 2019)

• Part I Basic Knot Theory.- Knots.- Knot and Link Invariants.- Framed Links.- Braids and the Braid Group.- Part II Quantum Knot Invariants.- R-Matrix Representations of Bn.- Knot Invariants through R-Matrix Representations of Bn.- Operator Invariants.- Ribbon Hopf Algebras.- Reshetikin-Turaev Invariants.- Part III Vassiliev Invarients.- The Fundamentals of Vassiliev Invariants.- Chord Diagrams.- Vassiliev Invariants of Framed Knots.- Jacobi Diagrams.- Lie Algebra Weight Systems.- Part IV The Kontsevich Invariant.- q-tangles.- Jacobi Diagrams on a 1-manifold.- A Construction of the Kontsevich Invariant.- Universality Properties of the Kontsevich Invariant.- Appendix A Background on Modules and Linear Algebra.- Appendix B Rewriting the Definition of Operator Invariants.- Appendix C Computations in Quasi-triangular Hopf Algebras.- Appendix D The Ribbon Hopf Algebra.- Appendix E A Proof of the Invariance of the Reshetikin-Turaev Invariants.

“This text is a comprehensive and well written introduction to quantum and Vassiliev invariants of knots. … There is sufficient detail for students and exercises. The text is also an excellent reference for researchers interested in quantum and Vassiliev invariants.” (Heather A. Dye, zbMATH 1425.57007, 2019)

• Part I Basic Knot Theory.- Knots.- Knot and Link Invariants.- Framed Links.- Braids and the Braid Group.- Part II Quantum Knot Invariants.- R-Matrix Representations of Bn.- Knot Invariants through R-Matrix Representations of Bn.- Operator Invariants.- Ribbon Hopf Algebras.- Reshetikin-Turaev Invariants.- Part III Vassiliev Invarients.- The Fundamentals of Vassiliev Invariants.- Chord Diagrams.- Vassiliev Invariants of Framed Knots.- Jacobi Diagrams.- Lie Algebra Weight Systems.- Part IV The Kontsevich Invariant.- q-tangles.- Jacobi Diagrams on a 1-manifold.- A Construction of the Kontsevich Invariant.- Universality Properties of the Kontsevich Invariant.- Appendix A Background on Modules and Linear Algebra.- Appendix B Rewriting the Definition of Operator Invariants.- Appendix C Computations in Quasi-triangular Hopf Algebras.- Appendix D The Ribbon Hopf Algebra.- Appendix E A Proof of the Invariance of the Reshetikin-Turaev Invariants.

“This text is a comprehensive and well written introduction to quantum and Vassiliev invariants of knots. … There is sufficient detail for students and exercises. The text is also an excellent reference for researchers interested in quantum and Vassiliev invariants.” (Heather A. Dye, zbMATH 1425.57007, 2019)

• Part I Basic Knot Theory.- Knots.- Knot and Link Invariants.- Framed Links.- Braids and the Braid Group.- Part II Quantum Knot Invariants.- R-Matrix Representations of Bn.- Knot Invariants through R-Matrix Representations of Bn.- Operator Invariants.- Ribbon Hopf Algebras.- Reshetikin-Turaev Invariants.- Part III Vassiliev Invarients.- The Fundamentals of Vassiliev Invariants.- Chord Diagrams.- Vassiliev Invariants of Framed Knots.- Jacobi Diagrams.- Lie Algebra Weight Systems.- Part IV The Kontsevich Invariant.- q-tangles.- Jacobi Diagrams on a 1-manifold.- A Construction of the Kontsevich Invariant.- Universality Properties of the Kontsevich Invariant.- Appendix A Background on Modules and Linear Algebra.- Appendix B Rewriting the Definition of Operator Invariants.- Appendix C Computations in Quasi-triangular Hopf Algebras.- Appendix D The Ribbon Hopf Algebra.- Appendix E A Proof of the Invariance of the Reshetikin-Turaev Invariants.