Latent profile analysis is a statistical modeling approach used to identify hidden subpopulations (i.e., latent profiles) within a population. These latent profiles are identified based on values of observed continuous variables, also known as profile indicators. While LPA is getting more popular in education sciences and psychology to group people based on similar characteristics, very little is known about the mathematical formulation. In this thesis, the mathematical foundations of LPA is introduced and explained. This leads to a discussion on the assumptions for the model. After investigating the mathematical foundations of LPA, we applied LPA to identify different profiles of motivation in a student population at Delft University of Technology. We used a set of survey data measuring four types of motivation (i.e., profile indicators). Results of the analysis showed that there are four different student motivational profiles, each consisting of a different combination of the four types of motivation.