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Symmetry's role in mechanics has always been important. In recent times, this aspect has accelerated because of new applications of symmetry techniques for studying integrable and chaotic systems, stability and bifurcation as well as for obtaining new insight into specific rigid, fluid, plasma and elastic systems. The new edition of this book, which lays the basic foundations for these topics, including reduction theory along with specific applications, has been extensively updated and includes new illustrations and exercises.