Explore the intricate world of quantization in this comprehensive lecture focusing on moduli spaces of flat connections. Delve into combinatorial quantization techniques and Batalin-Vilkovisky (BV) structures as presented by A. Alekseev from the University of Geneva. Gain insights into different perspectives on quantizing moduli spaces and their applications in mathematical physics. This 55-minute talk, part of the NCCR SwissMAP series, offers a deep dive into advanced mathematical concepts at the intersection of geometry, topology, and quantum theory.