Our focus in this book is on portfolio optimization as a core concept under investment: We discuss portfolio optimization based on the modern portfolio theory by Harry Markowitz. We take you through all the literature of portfolio optimization, and the theoretical foundations of the modern portfolio theory, we go a step further and explicitly take you through all the mathematics behind the mean-variance model, and finally, we discuss the entire process of developing the model and how to calculate the model parameters plus the actual application of the model; how to produce the frontier, the effect of including constraints or restrictions to the model as shown and discussed from the two resulting frontiers. Moreover special about this book is that; we test the applicability and validity of the mean-variance model to a young (developing) Securities Exchange like the Uganda Securities Exchange. Also we provide you with the VBA codes for developing the model and producing the efficient frontier. If you are a Financial Mathematics student, a CFA student, and any other persons interested in understanding the concept of portfolio optimization very well, this is the right book for you.