Public, online harassment takes many forms, but at its core are posts that are offensive, threatening, and intimidating. It is not an isolated problem. The Pew Research Center found 73% of people had witnessed harassment online, and a full 40% of people had experienced harassment directly. This research develops a method for analyzing the things people post online, and automatically detecting which posts fall into the category of severe public online harassment -- messages posted simply to disrupt, offend, or threaten others. This helps websites better limit what messages are posted and reduce the amount of harassment people experience online. The researchers develop a corpus of online comments from a number of media outlets and social media platforms where each post is labeled as harassing or non-harassing. Then, they apply a set of computational linguistic techniques that describe features of the message, including types of words and language structure, which is passed to rule-based and machine learning artificial intelligence systems for classification. The goal is to develop models that can automatically detect the public online harassment messages with high accuracy.