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 like polygons and polyhedra. For example, the symmetry group of a square includes rotations and reflections that map the square onto itself. Understanding these groups helps in various fields, including physics, chemistry, and art.