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This book deals with the many modern approaches to analyze ship dynamic stability and capsizing. The emphasis is on probabilistic assessment of ship dynamic stability. However, in order to evaluate ship dynamic stability and capsizing one must first formulate the nonlinear ship dynamics problem. This book will do much to raise the level of understanding of ship dynamic stability research to that of hydrodynamics and structures, and paves the way to consideration of ship stability safety as one aspect of the up-and-coming discipline of nonlinear dynamics of ships.