Chern classes are important concepts in differential geometry and algebraic topology, used to study vector bundles. They provide a way to associate a sequence of characteristic classes to a vector bundle, which can help in understanding its geometric properties. Chern classes are particularly useful in the context of complex manifolds and are named after the mathematician Shiing-Shen Chern. These classes can be computed using the curvature of a connection on the vector bundle. The first Chern class, for example, can be interpreted as a measure of the "twisting" of the bundle. Chern classes play a crucial role in various areas of mathematics, including K-theory and index theory.