Generating sets and presentations of automorphism groups of free Lie algebra

Let K be a field of characteristic zero, n,c be the positive integers and Fn, Ln,c be the free Lie algebra of rank n and free nilpotent Lie algebra of class c over K respectively. Denote by Mn,c the free metabelian and nilpotent Lie algebra of class c and rank n.In this thesis we find a generating set of Aut(L2,c) and using this generating set we obtain the relations this group and we give presentation of it, where c is small than 5.We find a presentation of Aut(M2,5) and we give a presentation of Aut(M2,c) by the same technique.And finally we find a generating set and defining relations of the automorphism group of Fn by using the generating set and defining relations of Aut(F2) .