Explore the second part of David Damanik's lecture on Gap Labelling, presented at the SMS 2023 conference focusing on Periodic and Ergodic Spectral Problems. Delve into advanced mathematical concepts as Damanik, from Rice University, continues his discussion on this crucial topic in spectral theory. Gain insights into the intricacies of gap labelling and its applications in periodic and ergodic systems. This hour-long talk, hosted by the Centre de recherches mathématiques (CRM), offers a deep dive into cutting-edge research in mathematical physics and spectral analysis.