A few years aga the authors started a project of a book on the theory of systems of one-dimensional singular integral equa- tions which was planned as a continuation of the monograph by one of the authors and N. Ya. Krupnik concerning scalar equa- tions. This set of notes was initiated as a chapter dealing with problems of factorization of matrix functions vis-a-vis appli- cations to systems of singular integral equations. Working systematically onthischapter and adding along the way new points of view, new proofs and results, we finally saw that the material connected with factorizations is...