In this thesis we start from the domination numbers of paths and cycles, to obtain that when can we get γ(P_n∪P_m )=γ(P_n )+γ(P_m ) and γ(P_n∪C_m )=γ(P_n )+γ(C_m ) respectively. Next, we get the relationship between the domination number of P_n □ P_m and P_n □ C_m as follows： Last part we obtain that the k-domination number of P_n □ C_m as follows Please see the thesis and electronic thesis for the results