The objective of the study is to apply Markov chain analysis to analyze student flow through King Abdul Aziz University (KAU) in Saudi Arabia, and to predict important metrics such as graduation and dropout rates. This objective arises from examination of the policies of KAU University. We begin with background information detailing the subject of study, then move into a general outline of stochastic processes. We then use these methods to construct a specific matrix of transition probabilities with data from the university student population. Finally, we discuss the calculation of the possibilities of transition between each level of study and the average time a student takes to complete each stage. The study uses Markov chains with these outcomes to analyze student retention data from the Department of Mathematics at KAU. From this analysis, the study will provide university policy recommendations that can be generalized to examine other universities.