Explore inverse problems for quantum graphs in this comprehensive lecture by Pavel Kurasov from Stockholm University. Delve into Ambartsumian-type results, trace formulas, and their implications for inverse problems. Examine local inverse problems, explicit formulas, and their limitations. Investigate inverse problems for trees, the process of gluing graphs, and extensions of symmetric operators. Learn about three specific inverse problems and their applications to graphs with cycles. Discover techniques for opening and cutting through cycles, gaining valuable insights into this fascinating area of mathematical physics.