This course explores the emerging mathematical foundations of algorithmic fairness across various decision-making contexts. Students will examine formal definitions of individual and (sub)group fairness, their relationships to each other and to the notion of bias, algorithms that provably satisfy them, and methods to audit existing algorithms for fairness. Application domains span social choice (resource allocation, voting, matching) and machine learning (classification, clustering). Students will apply these concepts through a project focused on examining fairness in a domain of their choice.