  In this article we provide a classification of the projective transformations
in $PSL(n+1,\Bbb{C})$ considered as automorphisms of the complex projective
space $\Bbb{P}^n$. Our classification is an interplay between algebra and
dynamics, which just as in the case of isometries of CAT(0)-spaces, can be
given by means of tree three types, namely: elliptic, parabolic and loxodromic.
We carefully describe the dynamic in each case, more precisely we determine the
corresponding Kulkarni's limit set, the equicontinuity region, the
discontinuity region and in some cases we provide families of maximal regions
where the respective cyclic group acts properly discontinuously. Also we
provide, in each case, some equivalents ways to classify the projective
transformations.
