Fourth-order tensors play an important role in continuum mechanics where they appear as elasticity and compliance tensors. In this section we define fourth-order tensors and learn some basic operations with them. To this end, we consider a set \(\boldsymbol{\mathcal {L}}\text {in}^n\) of all linear mappings of one second-order tensor into another one within \(\textbf{L}\text {in}^n\) . Such mappings are denoted by a colon as Linearmapping