Inequalities: Theory of Majorization and Its Applications Introduction Doubly Stochastic Matrices Schur Convex Functions Equivalent Conditions for Majorization Preservation and Generation of Majorization Rearrangements and Majorization Combinatorial Analysis Geometric Inequalities Matrix Theory Numerical Analysis Stochastic Majorizations Probabilistic Statistical and Other Applications Additional Statistical Applications Orderings Extending Majorization Multivariate Majorization Convex Functions and Some Classical Inequalities Stochastic Ordering Total Positivity Matrix Factorizations Compounds Direct Products and M Matrices Extremal Representations of Matrix Functions. This book’s first edition has been widely cited by researchers in diverse fields. The following are excerpts from reviews. “Inequalities: Theory of Majorization and its Applications” merits strong praise. It is innovative coherent well written and most importantly a pleasure to read. … This work is a valuable resource!” (Mathematical Reviews). “The authors … present an extremely rich collection of inequalities in a remarkably coherent and unified approach. The book is a major work on inequalities rich in content and original in organization.” (Siam Review). “The appearance of … Inequalities in 1979 had a great impact on the mathematical sciences. By showing how a single concept unified a staggering amount of material from widely diverse disciplines–probability geometry statistics operations research etc.–this work was a revelation to those of us who had been trying to make sense of his own corner of this material.” (Linear Algebra and its Applications). This greatly expanded new edition includes recent research on stochastic multivariate and group majorization Lorenz order and applications in physics and chemistry in economics and political science in matrix inequalities and in probability and statistics. The reference list has almost doubled.