In chapter 3 and 4, principal stresses are represented by a stress ellipsoid and no tensor notation was used yet. However, for the description of complex stress fields, tensor notation is much more powerful than the ellipsoid equation. Why this is so, is explained in the first part of this chapter. Subsequently vector notation is explained to allow description of normal and shear stress on an arbitrary plane. After that the stress tensor is defined. Finally different mathematical concepts to manipulate the stress tensor are explained.