Topological phases of matter are unique states of matter that arise from the geometric properties of their quantum states rather than their traditional characteristics like symmetry or particle interactions. These phases are characterized by topological invariants, which are properties that remain unchanged under continuous deformations, such as stretching or bending. One of the most well-known examples of topological phases is the quantum Hall effect, where electrons in a two-dimensional system exhibit quantized conductance at low temperatures and strong magnetic fields. Other examples include topological insulators, which conduct electricity on their surfaces while remaining insulating in their bulk, showcasing the fascinating interplay between topology and quantum mechanics.