Free nilpotent leibniz algebras

Let Fm(N) be the free left nilpotent Leibniz algebra of rank m .In this thesis firstly by examining the studies carried out , we gived definitions and basic theorems on Leibniz algebras. Then we also examined the structure, the automorphismis and the fixed point subalgebra of F(N) using the articles by Drensky, Cattaneo (2002) and Drensky, Papistas (2005). Finally, the set of fixed points of these automorphisms was obtained to making various calculations by using the automorphisms gived in Drensky,Papistas (2005).