David Futer, Efstratia Kalfagianni, and Jessica S. Purcell, A survey of hyperbolic knot theory -- Colin Adams, Spanning surfaces for hyperbolic knots in the 3-sphere -- Vaughan F.R. Jones, On the construction of knots and links from Thompson's groups -- Louis H. Kauffman, Virtual knot theory and virtual knot cobordism -- J\'ozef H. Przytycki, Knot Theory: from Fox 3-colorings of links to Yang-Baxter homology and Khovanov homology -- W. Edwin Clark and Masahico Saito, Algebraic and computational aspects of quandle 2-cocycle invariants -- Sam Nelson, A Survey of Quantum Enhancements -- Nafaa Chbili, From alternating to quasi-alternating links -- Alexander Stoimenov, Hoste's conjecture and roots of the Alexander polynomial -- Nancy Scherich, A survey of grid diagrams and a proof of Alexander's theorem -- Louis H. Kauffman and Sofia Lambropoulou, Extending the classical skein -- Maria Chlouveraki, From the framisation of the Temperley-Lieb algebra to the Jones polynomial: an algebraic approach -- Hoel Queffelec and Antonio Sartori, A note on the ${\mathfrak gl}_{m/n}$ link invariants and the HOMFLY-PT polynomial -- Mauro Spera, On the geometry of some braid group representations -- Celeste Damiani, Towards a version of Markov's theorem for ribbon torus-links in ${\Bbb R}^4$ -- Ioannis Diamantis, An alternative basis for the Kauffman bracket skein module of the solid torus via braids -- Bostjan Gabrovsek and Eva Horvat, Knot invariants in lens spaces -- Andrey M. Mikhovich, $QR$-presentations, schematization, conjurings and identity theorem for pro-$p$-groups -- Neslihan G\"ug\"umcu, Louis H. Kauffman, and Sofia Lambropoulou, A survey on knotoids, braidoids and their applications -- Rachel E. Ashley and Neil Osheroff, Regulation of DNA Topology by Topoisomerases: Mathematics at the Molecular Level -- Eleni Panagiotou, Topological entanglement and its relation to polymer material properties -- Stathis Antoniou, Louis H. Kauffman, and Sofia Lambropoulou, Topological surgery in the small and in the large.