This text provides an account of the theory and applications of multivariate reduced-rank regression, a tool of multivariate analysis that recently has come into increased use in broad areas of applications. In addition to a historical review of the topic, its connection to other widely used statistical methods, such as multivariate analysis of variance (MANOVA), discriminant analysis, principal components, canonical correlation analysis, and errors-in-variable models, is also discussed. Each chapter contains developments of basic theoretical results as well as details on computational procedures and other practical matters, illustrated with numerical examples drawn from disciplines such as biochemistry, marketing and finance. This book attempts to bring together the scope and range of the tool of multivariate reduced-rank regression, which has been in existence in varied forms since the mid-part of the 20th-century. This text should appeal to both practitioners and researchers, who may deal with moderate and high-dimensional multivariate data. It can used for seminar-type courses taken by advanced graduate students in statistics, econometrics, business and engineering.