Classification of Isometries of the Hilbert Metric

In this thesis we analyze the group of isometries of an Hilbert geometry. In the first part, we classify the elements of the group of projective isometries. In particular, these isometries are characterized by the behaviour of the translation lenght. In the second part, we explore the group of isometries in all its generality and we present a result by C. Walsh from 2017 which provides a characterization of the group of isometries in terms of the group of projective isometries.