This monograph is concerned with exchange rings in various conditions related to stable range. Diagonal reduction of regular matrices and cleanness of square matrices are also discussed. Readers will come across various topics: cancellation of modules, comparability of modules, cleanness, monoid theory, matrix theory, K-theory, topology, amongst others. This is a first-ever book that contains many of these topics considered under stable range conditions. It will be of great interest to researchers and graduate students involved in ring and module theories.