This book is an introduction to Γ-convergence and its applications. It is based on lecture notes from courses given by the author at the International School for Advanced Studies (SISSA) in Trieste and at the Istituto Nazionale di Alta Matematica (INDAM) in Rome. The text provides a systematic presentation of the basic theory of Γ-convergence, including the direct method in the calculus of variations, the general properties of Γ-limits in arbitrary topological spaces and in spaces with additional structures, the variational properties of Γ-convergence, the relationships between Γ-convergence of quadratic forms and G-convergence of the corresponding operators, the localization method for the study of Γ-limits of integral functionals, the problem of boundary conditions in the Γ-convergence of integral functionals, and the topologies related to Γ-convergence. The book covers both the coercive and non-coercive cases, and the examples given are chosen to illustrate the problems of the theory in the simplest possible way. The text also includes two applications of Γ-convergence: the main properties of the G-convergence of linear elliptic operators of second order and the proof of the homogenization formulas for integral functionals and elliptic operators. The book concludes with a guide to the literature and a bibliography. The author thanks Ennio De Giorgi for introducing him to the subject and for his guidance, as well as Giuseppe Buttazzo and Luciano Modica for their collaboration. He also acknowledges the help of his collaborators at SISSA and the typists who helped in preparing the manuscript.This book is an introduction to Γ-convergence and its applications. It is based on lecture notes from courses given by the author at the International School for Advanced Studies (SISSA) in Trieste and at the Istituto Nazionale di Alta Matematica (INDAM) in Rome. The text provides a systematic presentation of the basic theory of Γ-convergence, including the direct method in the calculus of variations, the general properties of Γ-limits in arbitrary topological spaces and in spaces with additional structures, the variational properties of Γ-convergence, the relationships between Γ-convergence of quadratic forms and G-convergence of the corresponding operators, the localization method for the study of Γ-limits of integral functionals, the problem of boundary conditions in the Γ-convergence of integral functionals, and the topologies related to Γ-convergence. The book covers both the coercive and non-coercive cases, and the examples given are chosen to illustrate the problems of the theory in the simplest possible way. The text also includes two applications of Γ-convergence: the main properties of the G-convergence of linear elliptic operators of second order and the proof of the homogenization formulas for integral functionals and elliptic operators. The book concludes with a guide to the literature and a bibliography. The author thanks Ennio De Giorgi for introducing him to the subject and for his guidance, as well as Giuseppe Buttazzo and Luciano Modica for their collaboration. He also acknowledges the help of his collaborators at SISSA and the typists who helped in preparing the manuscript.