Elasticity Theory is a branch of physics and engineering that studies how materials deform when forces are applied. It explains how objects stretch, compress, or twist and return to their original shape once the forces are removed. This behavior is crucial for understanding the mechanical properties of materials like metals, rubber, and polymers. The theory is based on the relationship between stress (force per unit area) and strain (deformation). Key concepts include Hooke's Law, which states that the deformation is proportional to the applied stress within the elastic limit of the material. This principle helps engineers design structures and products that can withstand various forces without permanent damage.