Table of contents : Front Matter....Pages i-x Matrices over the natural numbers: Values of the norms, classification, and variations....Pages 1-27 Towers of multi-matrix algebras....Pages 28-127 Finite von Neumann Algebras with Finite Dimensional Centers....Pages 128-181 Commuting sqares, subfactors, and the derived tower....Pages 182-231 Back Matter....Pages 232-288