Contains a unified exposition of spectral variation inequalities for matrices. The text provides a complete and self-contained collection of bounds for the distance between the eigenvalues of two matrices, which could be arbitrary or restricted to specific classes. Many basic results and techniques can be found in this book, making it a good reference for researchers and students. For the SIAM Classics edition, the author has added a new Supplements section, which includes recent results and discusses the important advances made in the study of theory, results, and proof techniques of spectral variation problems in the two decades since the book's original publication.