Abstarct: Let G be a finite group. The directed inclusion graph of cyclic subgroups of G, , is the digraph with vertex set of all cyclic subgroups of G, and for two distinct cyclic subgroups 〈a〉 and 〈b〉, there is an arc from 〈a〉 to 〈b〉 if and only if 〈b〉 ⊂ 〈a〉. The (undirected) inclusion graph of cyclic subgroups of G, , is the underlying graph of , that is, the vertex set is the set of all cyclic subgroups of G and two distinct cyclic subgroups 〈a〉 and 〈b〉 are adjacent if and only if 〈a〉 ⊂ 〈b〉 or 〈b〉 ⊂ 〈a〉. In this thesis, the planarity of (proper) inclusion graphs of cyclic subgroups of abelian groups are investigated and all abelian groups with planar graphs are classified. Also, some necessary conditions are provided for the groups that have planar inclusion graphs. In the following, the nilpotent groups with isomorphic inclusion graphs are considered. So, it is first shown that for both groups with isomorphic inclusion graphs, if one is cyclic, the other is cyclic. It is also proved that for any two finite abelian groups G and H, if and only if |π(G)|=|π (H)| and by a convenient permutation, the inclusion graphs of their sylow subgroups are isomorphic. And then, it is shown that their directed inclusion graphs are isomorphic too. Finally, we prove that non abelian nilpotent groups with isomorphic inclusion graphs have isomorphic directed inclusion graphs too.