This book is to provide the basic concepts and formulations related to the theory of elasticity, including the strain and stress tensors, the constitutive law, the principal strains and principal stresses, the plain stress and plain strain problems, etc. The theory of elasticity is an important basic subject for engineering students and serves as the basis for many advanced engineering courses, such as finite element method, the elastic-plastic mechanics, the continuum mechanics, etc. Therefore, understanding the basic concepts, the relevant formulations and mathematical preliminaries are important and crucial for students to understand the subsequent mechanics courses.