Abstract This chapter develops the necessary mathematics for describing general deformations that a solid body may undergo, a topic known as kinematics. Definitions of motion, displacement, velocity, and acceleration which are vectors, and the deformation gradient and displacement gradient which are tensors are given. The mapping of material vectors by the deformation gradient tensor as a basic concept in describing the large deformation kinematics of a deformable body is presented. The powerful polar decomposition theorem is discussed and applied to the deformation gradient tensor to show that it can be decomposed into a stretch followed by a rotation, or a rotation followed by a stretch. Non-linear measures of strain are defined in terms of the stretch tensors. The important case of small deformations, which results in linear measures of strain, is discussed. For small strains the important decomposition of the state of strain that separates a volumetric strain from a non-volumetric or deviatoric strain is presented.