Explore the fascinating intersection of mathematics and physics in this lecture on topological strings, knots, and quivers. Delve into the world of knot theory, beginning with closed loops in 3D manifolds and topological equivalence. Learn about polynomial knot invariants, including the HOMFLY-PT polynomial, and their connections to Chern-Simons theory. Discover cabling formulas and tackle exercises to reinforce understanding. Investigate the A-polynomial, recursion relations, and the volume conjecture, including its quantum counterpart. Examine knot homology and superpolynomials, with practical examples provided. Gain insights into the deep connections between quantum field theory, geometry, and representation theory in this comprehensive lecture from the International Centre for Theoretical Sciences' program on Quantum Fields, Geometry and Representation Theory.