Explore a comprehensive lecture on knot theory and group theory presented by V. O. Manturov. Delve into the intricate connections between knots and groups, focusing on the counterpart of the groups G^k_n in knot theory. Learn about key concepts such as the tetrahedron relation, four community dirty relation, and general position relations. Examine various examples of groups, including permutation groups, and their relevance to geometry and topology. Investigate invariants, invisible generators, and classical generators in knot theory. Discover the North counterpart and the main features of this year's theory. Gain insights into the applications of group theory in knot diagrams and calculations. This 53-minute talk offers a deep dive into advanced topics in quantum topology, suitable for mathematicians and researchers interested in the intersection of knot theory and group theory.