Singular cohomology is a mathematical tool used in the field of algebraic topology to study the properties of topological spaces. It assigns a sequence of abelian groups or vector spaces to a topological space, capturing information about its shape and structure. This is done by examining continuous maps from standard geometric shapes, called simplices, into the space. The main idea behind singular cohomology is to analyze how these simplices can be combined and related to one another. By using cochains, which are functions that assign values to these simplices, mathematicians can derive important invariants that help classify and differentiate topological spaces.