Cobordism theory is a branch of algebraic topology that studies the relationships between different manifolds. It focuses on the idea of cobordism, where two manifolds are considered equivalent if one can be transformed into the other by adding a "cobordism" manifold that connects them. This concept helps classify manifolds based on their dimensional properties and boundaries. In cobordism theory, manifolds are grouped into equivalence classes called cobordism classes. The theory has applications in various areas of mathematics, including homotopy theory and differential geometry. It provides a framework for understanding how manifolds can be related through continuous transformations.