Knot theory is the area of topology that deals with the study and classification of knots, and it is very closely related to the construction and classification of 3-manifolds. Since the ground-breaking discovery of the Jones polynomial, unexpected connections with operator algebras and Hecke algebras, statistical mechanics and quantum field theory have been found, new intriguing invariants of 3-manifolds have been constructed and the longstanding conjectures of Tait have been solved.