In this internship project will build a classical foundation for understanding how lattice defects (dislocations, disclinations) break crystal symmetries and organize phases of matter. The project starts by revisiting defect theory in classical media, then classifies defect types by the crystal symmetries they break, visualizes them across crystal structures, and studies their fusion rules (how defects merge/split). This groundwork sets up a possible PhD exploring quantum aspects: anomalies induced by defects on charge/spin degrees of freedom, experimental consequences in topological phases and spin liquids, and algebraic-topology tools to compute these anomalies.