This book treats the problem of how the Jordan structure of a matrix is changed by small analytic perturbation of this matrix. This topic has a long history and is important in
many applications. The book also contains the perturbation theory of isolated eigenvalues of linear operators in infinite dimensional spaces. The selfadjoint and normal cases are discussed separately. Attention is also given to the numerical
aspects and perturbation problems for operator bundles. The book contains a review of the necessary linear algebra and operator theory material, as well as an appendix with the complex analysis and algebraic basic material, thus making the volume self-contained.

The book will be of interest to a wide audience of mathematicians. Engineers, scientists and physicists alike should find this book useful. It can also be used for courses and seminars on the graduate and undergraduate level.