A classifying space is a topological space that serves as a universal model for a certain type of mathematical structure, often related to bundles or principal bundles. For example, the classifying space for vector bundles is denoted as BGL(n), which classifies all n-dimensional vector bundles over a topological space. This means that any vector bundle can be associated with a unique point in this space. In algebraic topology, classifying spaces help in understanding how different structures can be categorized and related to one another. They provide a way to study the properties of spaces through their associated bundles, making them essential in areas like homotopy theory and cohomology.