Explore quantum invariants of knots and their properties in this comprehensive lecture. Delve into the fascinating world of quantum topology as A. Slepcov presents an in-depth analysis of knot invariants and their unique characteristics. Gain insights into the mathematical foundations and applications of these quantum invariants, and discover how they contribute to our understanding of knot theory and related fields. Throughout the 1 hour and 31 minute presentation, examine various examples, proofs, and theoretical concepts that illuminate the intricate relationship between quantum mechanics and knot theory.