This text/reference is the most up-to-date volume on nonnegative matrices in print and presents much material that was previously available only in research papers. It is the only book to cover the van der Waerden conjecture on permanents. There is also coverage of doubly stochastic matrices and inverse problems. The material has abundant connections to graph theory, incidence geometry, stochastic processes, functional analysis, and quadratic forms. Each chapter contains a comprehensive set of problems and a substantial list of references.