The rank distance was introduced in 1985 by E. Gabidulin [1]. He determined a lower bound for the minimum rank distance of a code. Moreover, he constructed a class of codes which meet this bound: the so-called Gabidulin codes. In this paper, we first characterize the linear isometries for the rank distance. Then we determine the isometry group and the permutation group of Gabidulin codes of ful...