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This book offers a modern presentation of Continuum Mechanics, oriented towards numerical applications in the nonlinear analysis of solids, structures and fluid mechanics. General curvilinear coordinator kinematics of the continuum deformation, including pull-back / push-forward transformations between different configurations, stress and strain measures, balance principles, constitutive relations and variational principles are developed using general curvilinear coordinates. Although the mathematical presentation is quite rigorous; an effort is made to link formal developments with engineering physical intuition.