In this chapter we reduce the nonlinear theory of elasticity for large deformation to the linear theory for small deformation. The linear and angular momentum equations are re-derived using a direct and differential approach. A few theoretical aspects of the linear theory are examined such as the compatibility condition, maximum normal and shear tresses, displacement and stress formulations, principle of superposition, Clapeyron’s theorem, uniqueness theorem, reciprocal theorem and variational formulations.