Before introducing the “Theory of Elasticity: Basic Concepts and Formulations”, first of all, let’s have a look at the differences among “Theoretical Mechanics”, “Mechanics of Materials” and “Theory of Elasticity”. The “Theoretical Mechanics” is based on the assumption of mass point and rigid body, is mainly to investigate the kinematics of the object. Some representative examples in “Theoretical Mechanics” are celestial mechanics, etc. The “Mechanics of Materials” is based on the assumption of continuity, homogeneity, etc., and considers the deformation of the body. In “Mechanics of Materials”, simplified geometries (e.g., bar, beam, shell) and simplified forms (e.g., small deformation, plane section) are assumed to solve the simple problems. The “Theory of Elasticity” is an extension of the “Mechanics of Materials” and is to deal with complex scenarios, e.g., statics, dynamics, and it is the basis for all engineering designs and computations, the finite element method, the fracture mechanics and the plastic mechanics, etc.