A characteristic class is a mathematical concept used in the field of topology and differential geometry. It provides a way to associate algebraic invariants to vector bundles, which are structures that generalize the idea of a collection of vectors attached to each point of a manifold. These classes help in understanding the geometric and topological properties of the underlying space. Characteristic classes can be used to classify vector bundles up to isomorphism and are essential in various areas of mathematics, including algebraic topology and differential geometry. Common examples of characteristic classes include the Chern classes, Stiefel-Whitney classes, and Pontryagin classes, each serving different purposes in the study of manifolds and their properties.