Abstarct: Let G be a graph with vertex set V(G) and edge set E(G).We call a complete subgraph of G a clique of G. A clique partition of G is a set of cliques of G, which together contain each edge of G exactly once. The smallest cardinality of any clique partition of G is called the clique partition number of G. A clique cover of a graph G is a set of clique of G such that each edges of G is a appear in at least one clique. The smallest sie of a clique cover is called the clique cover number of G. In this thesis, we will investigate the clique partition and clique cover numbers of graphs. In this regard we prove two famous theorems, the Erdo ́s-Goodman-po ́sa theorem and Bruijn- Erdo ́s theorem. Also, the clique partition numbers of some especial families of graphs Will be computed.