Engineering Mechanics of Solids and Structures is essential for self-study and reference, setting out the underlying mechanical concepts, methods, and theories, applicable to a broad spectrum of structural and mechanical components - relevant to the analysis and design of a dome-like structure or a suspension bridge, the hull of a ship or a spacecraft, the mechanical component of an engine, or the power train of a vehicle. The principles are given thorough mathematical treatment, which demonstrates the limitations of the approximations and provides the tools for more precise analyses, then less mathematics is needed to show the behavior of simple structural components. This textbook covers both the Lagrangian and Newtonian approaches to the conditions of motion and equilibrium, offering the Lagrangean criteria of work and energy as the most effective means to formulate finite elements and other discrete approximations, which are amenable to digital computation. This gives advanced students in aerospace, mechanical, and civil engineering a solid foundation for the analysis and approximation of engineering problems, presented in a form that is both mathematically rigorous and physically meaningful.