Symmetry groups are mathematical structures that describe the symmetries of objects. They consist of a set of transformations, such as rotations and reflections, that can be applied to an object without changing its overall appearance. These transformations can be combined, and the group structure helps to understand how they relate to one another. In geometry, symmetry groups are essential for studying shapes and patterns. For example, the symmetry group of a square includes rotations by 90 degrees and reflections across its diagonals. Understanding these groups is crucial in fields like physics, chemistry, and art, where symmetry plays a significant role in the behavior and aesthetics of structures.