Explore the mathematical foundations and applications of topological Chern-Simons theory through this 40-minute conference presentation delivered as part of the Dublin Institute for Advanced Studies Summer Studentships final presentations. Delve into the dual perspectives and theoretical frameworks that characterize this important area of mathematical physics, examining how Chern-Simons theory connects topology, quantum field theory, and knot invariants. Learn about the key mathematical structures, computational techniques, and physical interpretations that make this theory fundamental to modern theoretical physics and mathematics. Gain insights into current research developments and applications in areas such as quantum gravity, condensed matter physics, and topological quantum computing through the collaborative presentation by three researchers presenting their summer research findings.