Deformation theory is a branch of mathematics that studies how geometric objects change shape while retaining certain properties. It focuses on understanding the small changes in structures, such as algebraic varieties or manifolds, and how these changes can be classified and analyzed. In particular, deformation theory is important in areas like algebraic geometry and string theory, where it helps mathematicians and physicists understand the stability and behavior of complex systems. By examining how objects deform, researchers can gain insights into their underlying structures and relationships.