I will try and present some concepts from knot theory, such as the coloured Jones polynomial and Kauffman bracket skein modules, so as to explain the content of the AJ-conjecture (or quantum volume conjecture), which is a statement about a non-commutative version of the \(A\)-polynomial. The talk will be mainly based on T. Le, The coloured Jones polynomial and the \(A\)-polynomial of knots, Adv. Math. 207 (2006) 782-804. If time permits, I will comment on work by Gukov et al which refines or categorifies the quantum \(A\)-polynomial.