Perturbation Bounds for Matrix Eigenvalues 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 special classes. The book's emphasis on sharp estimates, general principles, elegant methods, and powerful techniques, makes it a good reference for researchers and students. For the SIAM Classics edition, the author has added over 60 pages of material covering recent results and discussing the important advances made in the theory, results, and proof techniques of spectral variation problems in the two decades since the book's original publication. This updated edition is appropriate for use as a research reference for physicists, engineers, computer scientists, and mathematicians interested in operator theory, linear algebra, and numerical analysis. It is also suitable for a graduate course in linear algebra or functional analysis.