This chapter introduces the concept of Γ-convergence, a central topic in variational analysis and its applications. The book, authored by Gianni Dal Maso, provides a comprehensive and systematic introduction to Γ-convergence, covering its foundational aspects and key properties. The content is structured into several chapters, each focusing on different aspects of Γ-convergence, including: 1. **Direct Method in Calculus of Variations**: Introduces the basic principles and techniques used in the calculus of variations. 2. **Γ-convergence in Topological Spaces**: Discusses the general properties of Γ-limits in arbitrary topological spaces. 3. **Variational Properties of Γ-convergence**: Explores the variational aspects of Γ-convergence. 4. **Γ-convergence of Quadratic Forms and G-convergence of Operators**: Connects Γ-convergence of quadratic forms with G-convergence of operators. 5. **Localization Method for Integral Functionals**: Focuses on the localization method for studying Γ-limits of integral functionals. 6. **Boundary Conditions in Γ-convergence**: Addressing the problem of boundary conditions in the context of integral functionals. 7. **Topologies Related to Γ-convergence**: Introduces the topologies associated with Γ-convergence. The book also includes applications of Γ-convergence, such as the main properties of G-convergence of linear elliptic operators and the proof of homogenization formulas for integral functionals and elliptic operators. The author acknowledges the influence of Ennio De Giorgi and other collaborators, highlighting their contributions to the development of the theory and the completion of the book.This chapter introduces the concept of Γ-convergence, a central topic in variational analysis and its applications. The book, authored by Gianni Dal Maso, provides a comprehensive and systematic introduction to Γ-convergence, covering its foundational aspects and key properties. The content is structured into several chapters, each focusing on different aspects of Γ-convergence, including: 1. **Direct Method in Calculus of Variations**: Introduces the basic principles and techniques used in the calculus of variations. 2. **Γ-convergence in Topological Spaces**: Discusses the general properties of Γ-limits in arbitrary topological spaces. 3. **Variational Properties of Γ-convergence**: Explores the variational aspects of Γ-convergence. 4. **Γ-convergence of Quadratic Forms and G-convergence of Operators**: Connects Γ-convergence of quadratic forms with G-convergence of operators. 5. **Localization Method for Integral Functionals**: Focuses on the localization method for studying Γ-limits of integral functionals. 6. **Boundary Conditions in Γ-convergence**: Addressing the problem of boundary conditions in the context of integral functionals. 7. **Topologies Related to Γ-convergence**: Introduces the topologies associated with Γ-convergence. The book also includes applications of Γ-convergence, such as the main properties of G-convergence of linear elliptic operators and the proof of homogenization formulas for integral functionals and elliptic operators. The author acknowledges the influence of Ennio De Giorgi and other collaborators, highlighting their contributions to the development of the theory and the completion of the book.