Grothendieck–Chow motives provide a framework for studying algebraic varieties through correspondences rather than ordinary morphisms, allowing one to isolate and compare their essential geometric and cohomological features. They unify many classical invariants in algebraic geometry, such as Chow groups, K-theories, and oriented cohomology theories into a single categorical setting. Motivic decompositions often reveal hidden geometric structures and symmetries of varieties, especially for quadrics and various flag varieties. This mini course will give an introduction to Grothendieck–Chow motives and their applications.…