Explore advanced concepts in quantum field theory and non-perturbative physics in this comprehensive lecture. Delve into topics such as instability and divergence of perturbation theory, Borel summation, resurgent trans-series, and the Euler-Heisenberg effective action. Examine the IR renormalon puzzle in asymptotically free QFT and investigate topological molecules in spatially compactified theories. Learn about analytic continuation of path integrals, the Darboux theorem, and resurgence in quantum mechanics. Discover connections between perturbative and non-perturbative sectors, and explore applications of resurgence in supersymmetric quantum mechanics. Gain insights into cutting-edge research in theoretical physics from expert Gerald Dunne at the International Centre for Theoretical Sciences.