Dissertation (MSc Mathematics)The purpose of this dissertation is to survey Analytic Hierarchy Process (AHP) as the tool used in decision making. The decision making process involves evaluating alternatives or criterion by selecting the best option. The AHP is the decision making technique which involves both subjective human judgments and objective evaluation merely by Eigen vector and then examines the consistency of the evaluation by Eigen Value. In this dissertation we have shown in details methods of AHP and how are they being used to determine the priorities of preferences of decision makers. The methods explained in this dissertation are Sum Method (SM), Eigen value Method (EM), and Geometric mean (GM) which sometimes is known as the Logarithmic Least Square Method (LLSM). Furthermore we have explained the significant of the AHP in decision making process and we have shown how it is an appropriate tool to address the prioritization problem in order to make better decisions in various fields by showing the use of qualitative and quantitative criteria in evaluation. For more elaboration of the AHP, we have used some examples found in literature reviews used by other researchers in order to determine the priorities and lastly we have used an example of selecting the best smart mobile phone from four alternatives. The data used in this example of selecting smart mobile phones were obtained by collecting data from customers who possess and who are familiar with the smart mobile phones. So the AHP helps decision makers choose the best product from several options. The dissertation also surveys LLSM, EM and SM by checking their similarity or different in ranking the alternatives and checking whether they can results either the same or the different priority weights.