The book "Nonlinear Problems in Elasticity" by Stuart S. Antman, published in its second edition, is a comprehensive treatise on the mathematical and physical aspects of nonlinear elasticity. The book aims to update and refine the content of the first edition, addressing new developments in the field while correcting errors and improving the exposition. It is designed to be accessible to a wide audience, including scientists, engineers, and mathematicians, with a focus on well-formulated, specific problems in nonlinear elasticity. The author's approach is to provide a general theory for each type of elastic body, carefully formulate specific problems, introduce relevant mathematical methods, and conduct rigorous analyses. The book covers topics such as strings, rods, shells, and three-dimensional bodies, following a historical development order. It also includes detailed formulations of three-dimensional continuum mechanics, the theory of nonlinear elasticity, large-strain plasticity, and general theories of rods and shells. Key features of the book include: - A focus on geometrically exact theories and global analysis of well-set problems. - The use of global bifurcation theory, continuation methods, and perturbation methods. - An emphasis on the qualitative behavior of solutions and the impact of constitutive functions. - A wealth of exercises designed to challenge and extend the reader's understanding. The book is structured into several chapters, each covering specific aspects of nonlinear elasticity, from foundational concepts to advanced topics, and includes appendices on linear and nonlinear analysis, degree theory, and other relevant mathematical tools.The book "Nonlinear Problems in Elasticity" by Stuart S. Antman, published in its second edition, is a comprehensive treatise on the mathematical and physical aspects of nonlinear elasticity. The book aims to update and refine the content of the first edition, addressing new developments in the field while correcting errors and improving the exposition. It is designed to be accessible to a wide audience, including scientists, engineers, and mathematicians, with a focus on well-formulated, specific problems in nonlinear elasticity. The author's approach is to provide a general theory for each type of elastic body, carefully formulate specific problems, introduce relevant mathematical methods, and conduct rigorous analyses. The book covers topics such as strings, rods, shells, and three-dimensional bodies, following a historical development order. It also includes detailed formulations of three-dimensional continuum mechanics, the theory of nonlinear elasticity, large-strain plasticity, and general theories of rods and shells. Key features of the book include: - A focus on geometrically exact theories and global analysis of well-set problems. - The use of global bifurcation theory, continuation methods, and perturbation methods. - An emphasis on the qualitative behavior of solutions and the impact of constitutive functions. - A wealth of exercises designed to challenge and extend the reader's understanding. The book is structured into several chapters, each covering specific aspects of nonlinear elasticity, from foundational concepts to advanced topics, and includes appendices on linear and nonlinear analysis, degree theory, and other relevant mathematical tools.