Cohomology is a mathematical concept used in algebraic topology to study the properties of topological spaces. It provides a way to assign algebraic structures, such as groups or rings, to these spaces, allowing mathematicians to analyze their shape and features. Cohomology groups can reveal information about the number of holes in a space and its overall structure. One of the key tools in cohomology is the de Rham cohomology, which connects differential forms with topological properties. Another important aspect is the Cech cohomology, which uses open covers to define cohomological groups. These methods help in understanding complex spaces in a more manageable way.