Combinatorial group theory is a branch of mathematics that studies groups, particularly infinite groups, through the use of combinatorial techniques. It focuses on group presentations by generators and relations. This field investigates structural properties of groups by analyzing their presentations, the properties of words in the generators, and associated combinatorial objects such as Cayley graphs. Key problems addressed include algorithmic decision problems like the word problem, conjugacy problem, and isomorphism problem, as well as structural questions about subgroups and quotients. The significance lies in providing algorithmic and geometric insights into group structure and establishing fundamental connections between group theory, topology (via fundamental groups), and logic.