Algorithmic fairness is receiving significant attention in the academic and broader literature due to the increasing use of predictive algorithms, including those based on artificial intelligence. One benefit of this trend is that algorithm designers and users have a growing set of fairness measures to choose from... However, this choice comes with the challenge of identifying how the different fairness measures relate to one another, as well as the extent to which they are compatible or mutually exclusive. We describe some of the most widely used fairness metrics using a common mathematical framework and present new results on the relationships among them. The results presented herein can help place both specialists and non-specialists in a better position to identify the metric best suited for their application and goals. (read more)