The present book deals with canonical factorization of matrix and operator functions that appear in state space form or that can be transformed into such a form. A unified geometric approach is used. The main results are all expressed explicitly in terms of matrices or operators, which are parameters of the state space representation. The applications concern different classes of convolution equations. A large part the book deals with rational matrix functions only. von Bart, Harm und Gohberg, Israel und Kaashoek, M. A. und Ran, André C. M.