Abstarct: Let vertices u and v be at distance two apart in a graph G, and let x be a common neighbor of u and v. The operation of removing the edges ux and vx from G, while adding the edge uv to G is called edge lifting. In chapter 1, we state some basic and elementary consept which we use for the next chapter. In chapter 2, we study the effect of edge lifting on the Domination number of the Graphs. In chapter 3, we inveswtigate the effect of edge lifting on the total Domination of the Graphs.