This thesis studies the relationship between extremists groups, their presence online, their ability to radicalize individuals, and the implications of this relationship. Data was collected from Twitter related to two significant events claimed by ISIS or ISIS supporters: the 2015 terrorist attacks in Paris and the 2017 Battle of Marawi in the Philippines. The sample of tweets was then broken down into four different "phases" of radicalization by using key indicator terms of each phase. Using both an analysis of time-series trends and negative binomial regression I examine the relationship between the temporal proximity to each event and the number of tweets in each phase of radicalization. The results are inconclusive: there are few clear trends in the time-series analysis, and no statistically significant relationships. I offer possible explanations for the absence of significant relationships, and I conclude that the results nonetheless demonstrate the potential of this type of analysis in the future. Extremist groups continue to operate online, and understanding how they do so may be key to stopping them from radicalizing more individuals.