The mathematical approach to the study of hierarchies presents the theoretical basis for many important areas of current scientific investigation. Biology has benefited from this research and has also stimulated the mathematical study of hierarchies. This collection presents papers devoted to theoretical, algorithmical, and application issues related to: reconstructing hierarchies (trees or ranking) from (dis)similarity or entity-to-character data; using hierarchies for modeling evolution and other processes; and, combining (gene) trees. The papers in this volume provide a contemporary sample of many new results in hierarchy theory with applications in biology, psychology, data analysis, and systems engineering.It's features include: mathematical treatment of hierarchies in several interconnected frameworks: set systems, linear subspaces, graph objects, and tree metrics; the relationship of hierarchies to many issues of current application-from learning robots to wavelets to intron evolution to the evolution of language; and, solutions to several important problems.
