2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100830We study relationships between the colored Jones polynomial and the A-polynomial of a knot. We establish for a large class of 2-bridge knots the AJ conjecture (of Garoufalidis) that relates the colored Jones polynomial and the A-polynomial. Along the way we also calculate the Kauffman bracket skein module of all 2-bridge knots. Some properties of the colored Jones polynomial of alternating knots are established.Typos and minor mistakes corrected. To appear in Advances in MathematicsGeometric TopologyQuantum Algebra57M25text