Quantum groups are mathematical structures that arise in the study of quantum mechanics and representation theory. They generalize the concept of groups, which are fundamental in describing symmetries in mathematics and physics. Quantum groups incorporate non-commutative algebra, meaning that the order of operations matters, reflecting the principles of quantum theory. These structures play a significant role in various areas, including quantum field theory and string theory. They provide a framework for understanding symmetries in a quantum context, allowing physicists to explore new phenomena and develop theories that extend beyond classical physics.