Quantum topology is a branch of mathematics which connects ideas from quantum field theory with low-dimensional topology. It rose to prominence in the 1980′s when the newly discovered Jones polynomial invariant of knots and links, which arose from ideas in operator algebras, was given a geometric explanation by Witten as being the partition function in a three-dimensional quantum field theory known as Chern-Simons theory. Soon other “quantum invariants” of geometric structures were discovered and put into this framework, such as Floer homology, Gromov-Witten theory, Seiberg-Witten theory andÂ Khovanov homology.