Crowd behavior analysis, a subdomain of human activity recognition, is a broad topic in computer vision that includes crowd management, public space design, virtual environments, visual surveillance, and intelligent environments. Recent areas of high interest include interactions between small groups of people and large crowds of people at gatherings such as a sporting venue, concert, or religious pilgrimage. Tragic incidents, such as the stampeding that occurred at the 2010 Loveparade concert and the multiple incidents that have occurred at the Jamarat Bridge necessitate a need for crowd analysis. Since 1994, over 1500 people have been killed or injured in stampedes and related incidents during the Hajj. Advances in crowd analysis research have improved and insured the safety of individuals of future events. Our research is aimed at preventing such incidents from occurring through real-time detection of abnormal crowd behavior.In this dissertation, we present two methods for abnormal behavior detection in an effort to reduce the number of tragic incidents occurring in large crowds. The first method is based upon deviations in primary or dominant motion paths within the scene. We implement a method for dominant motion extraction based upon optical flow clustering and develop a matching algorithm to compare dominant motion paths at various points in the video. Our second method, using a particle advection model for local motion, predicts the location of a particle based upon its previous motion. By measuring the distance between the predicted trajectory and the observed trajectory, we are able to determine the presence of abnormal behavior. This method addresses several deficiencies in our first. Lastly, we present a method for video clustering of crowd motion based upon optical flow. Our methodology uses histograms of optical flow to train a support vector machine to classify types of dominant motion. Using these classes, we cluster similar videos using hierarchical methods. Experiments use hundreds of videos from several public video motion data sets.