This book provides a comprehensive introduction to the theoretical and practical aspects of multilinear subspace learning (MSL). It not only details recent advances in MSL, but also explores future developments and emerging applications. The authors address multilinear algebra fundamentals, multilinear projections, formulation of the MSL framework, MSL optimality criterion construction, and MSL algorithms and solutions. Emphasizing fundamental concepts and system-level perspectives, the text provides a foundation upon which solutions for many of today s most interesting and challenging problems in massive multidimensional data processing can be built.