Cohomology is a branch of algebraic topology and algebraic geometry that studies the properties of geometric objects through algebraic techniques. It provides a way to measure the "holes" in a space or the ways in which a space may be twisted or curved. Cohomology can be thought of as the dual concept to homology, which studies the cycles and boundaries of a given space. In cohomology, one studies the dual objects to these cycles and boundaries - cocycles and coboundaries. By studying these dual objects, cohomology provides a way to classify and understand geometric spaces in a more abstract and algebraic way. Cohomology has many applications in mathematics, including in the study of differential geometry, algebraic geometry, and algebraic topology. It is a powerful tool for understanding the structure of spaces and their symmetries, and has connections to many other areas of mathematics.