Explore the fundamental concepts of topological phases of matter in this 84-minute lecture delivered by Chong Wang from the Perimeter Institute as part of the Journeys into Theoretical Physics program at IFT/ICTP-SAIFR. Delve into the theoretical foundations that govern exotic states of matter where topology plays a crucial role in determining physical properties. Learn about the mathematical frameworks and physical principles that characterize these unique quantum phases, which have revolutionized our understanding of condensed matter physics and opened new avenues for quantum technologies. Gain insights into how topological invariants protect certain properties of materials against local perturbations, making them particularly interesting for both fundamental physics and potential applications in quantum computing.