Geometric Group Theory is a branch of mathematics that studies groups by examining their geometric properties and the spaces they act upon. It combines concepts from group theory, topology, and geometry to understand the structure and behavior of groups through visual and spatial means. One of the key ideas in this field is the use of Cayley graphs, which represent groups as geometric objects. Researchers explore how groups can be represented as symmetries of spaces, such as hyperbolic spaces or manifolds, leading to insights about their algebraic properties and relationships with other mathematical structures.