Social Network Analysis is a compilation of methods used to identify and analyze patterns in social network systems. This article serves as a primer on foundational social network concepts and analyses and builds a case study on the global Islamist terrorist network to illustrate the use and usefulness of these methods. The Islamist terrorist network is a system composed of multiple terrorist organizations that are socially connected and work toward the same goals. This research utilizes traditional social network, as well as small-world, and scale-free analyses to characterize this system on individual, network and systemic levels. Leaders in the network are identified based on their positions in the social network and the network structure is categorized. Finally, two vital nodes in the network are removed and this version of the network is compared with the previous version to make implications of strengths, weaknesses and vulnerabilities. The Islamist terrorist network structure is found to be a resilient and efficient structure, even with important social nodes removed. Implications for counterterrorism are given from the results of each analysis.