Group representations are mathematical tools used to study the symmetries of objects through linear transformations. They allow us to represent elements of a group as matrices, making it easier to analyze their properties and behaviors. This approach is particularly useful in fields like physics, where symmetries play a crucial role in understanding fundamental forces and particles. In essence, a group representation translates abstract group elements into concrete actions on vector spaces. By examining these representations, mathematicians and scientists can uncover deeper insights into the structure of groups and their applications in various domains, including chemistry and computer science.