The book "An Introduction to the Mathematical Theory of Inverse Problems" by Andreas Kirsch is a comprehensive text on inverse problems, covering both linear and nonlinear cases. It is part of the Applied Mathematical Sciences series, edited by several prominent mathematicians. The book is intended for users of mathematics, mathematicians interested in applications, and student scientists. It provides an introduction to the mathematical theory of inverse problems, focusing on current developments and practical applications. The third edition, published in 2021, includes new chapters and sections, such as a chapter on nonlinear techniques for locally improperly posed equations in Hilbert spaces and a section on interior transmission eigenvalues. The book also corrects mistakes and ambiguities from previous editions and includes new material on topics like electrical impedance tomography and inverse scattering theory. The second edition, published in 2011, expands on the first edition by adding new chapters on electrical impedance tomography and inverse scattering theory. It includes the Factorization Method, a powerful technique for solving nonlinear inverse problems. The book also discusses regularization methods for ill-posed problems, including Tikhonov regularization, Landweber iteration, and spectral cutoff. The first edition, published in 1996, introduces the basic concepts of inverse problems, including the distinction between direct and inverse problems, and the concept of ill-posed problems. It discusses regularization methods for linear ill-posed problems and provides an overview of inverse spectral theory and inverse scattering theory. The book is organized into chapters that cover various aspects of inverse problems, including regularization theory, discretization methods, nonlinear inverse problems, inverse eigenvalue problems, and inverse scattering problems. It includes a detailed discussion of the Factorization Method, which is particularly useful for solving inverse problems in electrical impedance tomography and inverse scattering theory. The book also includes an appendix with basic facts from functional analysis, which is essential for understanding the mathematical concepts discussed in the text. The references section provides a list of important works in the field of inverse problems, including monographs, proceedings, and survey articles. The book is a valuable resource for mathematicians, physicists, and engineers interested in the theory and application of inverse problems.The book "An Introduction to the Mathematical Theory of Inverse Problems" by Andreas Kirsch is a comprehensive text on inverse problems, covering both linear and nonlinear cases. It is part of the Applied Mathematical Sciences series, edited by several prominent mathematicians. The book is intended for users of mathematics, mathematicians interested in applications, and student scientists. It provides an introduction to the mathematical theory of inverse problems, focusing on current developments and practical applications. The third edition, published in 2021, includes new chapters and sections, such as a chapter on nonlinear techniques for locally improperly posed equations in Hilbert spaces and a section on interior transmission eigenvalues. The book also corrects mistakes and ambiguities from previous editions and includes new material on topics like electrical impedance tomography and inverse scattering theory. The second edition, published in 2011, expands on the first edition by adding new chapters on electrical impedance tomography and inverse scattering theory. It includes the Factorization Method, a powerful technique for solving nonlinear inverse problems. The book also discusses regularization methods for ill-posed problems, including Tikhonov regularization, Landweber iteration, and spectral cutoff. The first edition, published in 1996, introduces the basic concepts of inverse problems, including the distinction between direct and inverse problems, and the concept of ill-posed problems. It discusses regularization methods for linear ill-posed problems and provides an overview of inverse spectral theory and inverse scattering theory. The book is organized into chapters that cover various aspects of inverse problems, including regularization theory, discretization methods, nonlinear inverse problems, inverse eigenvalue problems, and inverse scattering problems. It includes a detailed discussion of the Factorization Method, which is particularly useful for solving inverse problems in electrical impedance tomography and inverse scattering theory. The book also includes an appendix with basic facts from functional analysis, which is essential for understanding the mathematical concepts discussed in the text. The references section provides a list of important works in the field of inverse problems, including monographs, proceedings, and survey articles. The book is a valuable resource for mathematicians, physicists, and engineers interested in the theory and application of inverse problems.