Character theory is a branch of mathematics that studies the representations of groups through linear algebra. It focuses on the characters of a group, which are special functions that provide important information about the group's structure. By analyzing these characters, mathematicians can gain insights into the properties of the group, such as its symmetry and how it can be decomposed into simpler components. In the context of group theory, character theory helps in understanding how different representations relate to one another. It is particularly useful in the study of finite groups and has applications in various fields, including physics and chemistry, where symmetry plays a crucial role in understanding molecular structures and behaviors.