In this chapter we establish the nonlinear theory of elasticity for large deformation. It begins with balance laws in integral form and then derives their differential form. The general jump conditions at a discontinuity surface are obtained. The third-order theory for weak nonlinearity and the linear theory for small fields on a finite bias are also presented. This chapter includes the linear theory in the following chapter as a special case. Most of this chapter may be skipped if the nonlinear theory is of no interest, except the sections on the Cauchy stress principle and stress tensor.