Explore a comprehensive lecture on instanton Floer homology and its applications in 3-manifold topology. Delve into the powerful invariant introduced by Floer in the 1980s, which has proven instrumental in solving problems like the Property P conjecture. Examine the conjectured isomorphism between instanton Floer homology and other Floer theories, focusing on the surgery formula as a key property. Learn about a newly presented surgery formula for instanton theory and its practical applications in computing instanton Floer homology and studying SU(2)-representations of fundamental groups in 3-manifolds. Gain insights from Stanford University researcher Zhenkun Li on this cutting-edge topic in low-dimensional topology.