The Applied Mathematical Sciences series, edited by renowned mathematicians, aims to provide introductory and up-to-date books for users of mathematics, mathematicians interested in applications, and student scientists. The series focuses on topics of current interest, featuring a tutorial style and clear exposition. The third edition of "An Introduction to the Mathematical Theory of Inverse Problems" by Andreas Kirsch, published by Springer Nature Switzerland AG, covers the rapid developments in the field of inverse problems. The book introduces basic principles and developments, with a focus on linear ill-posed problems and nonlinear inverse problems. New content includes a chapter on locally improperly posed nonlinear equations in Hilbert spaces, a section on interior transmission eigenvalues, and corrections to previous editions. The book is designed to serve as a textbook for graduate courses and includes detailed proofs and numerical examples.The Applied Mathematical Sciences series, edited by renowned mathematicians, aims to provide introductory and up-to-date books for users of mathematics, mathematicians interested in applications, and student scientists. The series focuses on topics of current interest, featuring a tutorial style and clear exposition. The third edition of "An Introduction to the Mathematical Theory of Inverse Problems" by Andreas Kirsch, published by Springer Nature Switzerland AG, covers the rapid developments in the field of inverse problems. The book introduces basic principles and developments, with a focus on linear ill-posed problems and nonlinear inverse problems. New content includes a chapter on locally improperly posed nonlinear equations in Hilbert spaces, a section on interior transmission eigenvalues, and corrections to previous editions. The book is designed to serve as a textbook for graduate courses and includes detailed proofs and numerical examples.