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 third manifold, called a cobordism. This concept helps classify manifolds based on their dimensional properties and boundaries. In cobordism theory, manifolds are grouped into equivalence classes, known as cobordism classes. These classes can be analyzed using algebraic structures, such as homology and cohomology groups, which provide tools for understanding the topological features of manifolds. This theory has applications in various areas of mathematics and theoretical physics.