Part a offers an introduction to knot theory: the problem of classification of knots, different knot types, basic (classical) invariants, and some elements of knot concordance. Part b moves from classical to quantum invariants: the Jones polynomial, colored Jones polynomial, and then more general quantum group invariants of knots and 3-manifolds. Part b also includes introduction to R-matrices, the Yang-Baxter equation, the Drinfeld-Kohno theorem and, if time permits, elements of categorification.