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...