Rakesh Vohra University of Pennsylvania Matching problems have played a central role in thinking about the terms of trade in two sided markets. Models are of two kind. One where the only information about agents preferences are ordinal and the other where they are cardinal. Until recently they have developed using different techniques. In this series of presentations I will provide a unified account of the two and introduce some of the main techniques from linear programming and fixed points. Chief among these is Scarf’s lemma.