Characteristic classes are mathematical tools used in topology and differential geometry to study vector bundles. They provide a way to classify these bundles based on their geometric properties, helping to understand how they can be twisted or deformed. These classes are often represented as cohomology classes, which are algebraic structures that capture information about the shape and structure of spaces. Important examples of characteristic classes include the Chern classes, Stiefel-Whitney classes, and Euler classes, each serving different purposes in the study of manifolds and their associated bundles.