A Symmetry Group is a mathematical concept that describes the set of all symmetries of a given object. These symmetries include transformations such as rotations, reflections, and translations that leave the object's structure unchanged. Symmetry groups are essential in various fields, including geometry, physics, and chemistry, as they help to understand the properties and behaviors of objects. In group theory, a branch of mathematics, symmetry groups are classified based on their properties. For example, the symmetry group of a square includes four rotations and four reflections. Understanding these groups allows mathematicians and scientists to analyze patterns and predict outcomes in systems, such as those found in crystallography and molecular structures.