Surgery Theory is a branch of mathematics that studies the properties of manifolds, particularly in relation to their topology and geometry. It focuses on how certain operations, like cutting and pasting, can change the structure of these spaces. This theory helps mathematicians understand complex shapes and their relationships. One key aspect of Surgery Theory is the concept of surgery itself, which involves modifying a manifold by removing a piece and replacing it with another. This process can reveal important information about the manifold's characteristics, such as its homotopy and homology groups, which are essential for classifying different types of spaces.