This study provides a comprehensive explanation about one of the important multi-criteria decision-making technique entitled Analytical Hierarchy Process (AHP). This chapter will include a summary of the steps required to carry out the mathematical computation of AHP for problems with both consistency and inconsistency in the decision-maker’s preferences. Hierarchy design, prioritization, criteria weights, and consistency are all extensively taken into consideration. Further elaborations regarding the different applications of the AHP process will also be discussed, including various fields such as business-related decision making and decision theory in the field of medicine. The limitations imposed by the analytical hierarchy process are also discussed.