"An Introduction to Differential Geometry with Applications to Elasticity" is a specialized book that deals with the fundamentals of differential geometry and its applications in elasticity theory. It provides a comprehensive introduction to the subject, particularly addressing the Korn inequality in curvilinear coordinates and the modeling of thin elastic shells. The structure of the book is clearly organized, with the initial chapters introducing basic concepts of differential geometry, while the later chapters present specific applications and mathematical models. The topics covered are of interest to both students and professionals who are engaged with the mathematical aspects of elasticity and geometry. The book is a valuable resource for anyone seeking a deeper understanding of the mathematical foundations of elasticity theory.