Group cohomology is a mathematical concept that studies the properties of groups using cohomological techniques. It provides a way to classify and understand extensions of groups and their representations. By associating algebraic structures, called cochains, to groups, mathematicians can derive important invariants that reveal information about the group's structure. The main idea is to analyze how groups act on certain algebraic objects, such as abelian groups or modules. This action leads to the construction of cohomology groups, which capture essential features of the group. Group cohomology has applications in various fields, including topology, algebraic geometry, and number theory.