These lecture notes give an overview of the basic results for error correcting codes in the rank metric. The notes are divided into four chapters, where in the first one we give an introduction and explain the linear network coding channel and how matrix codes equipped with the rank metric can be used in such channels to correct errors occurring during communication. In the second chapter we introduce the general notions and properties of rank-metric codes, the third one deals with the class of Gabidulin codes and the related linearized polynomials, and the fourth chapter gives an introduction to rank metric code-based cryptography.
