Topological phases are distinct states of matter that arise from the global properties of a system rather than its local characteristics. These phases are characterized by topological invariants, which are mathematical quantities that remain unchanged under continuous deformations. Examples include the quantum Hall effect and topological insulators, where the surface states exhibit unique conductive properties. In topological phases, the behavior of particles can be robust against disturbances, such as impurities or changes in shape. This resilience is due to the underlying topology of the system, which protects certain features. Researchers study these phases to explore new materials and potential applications in quantum computing.