Matching Theory is a concept in economics and game theory that studies how agents pair up in various markets, such as job seekers with employers or students with schools. It focuses on the preferences of each party and how these preferences influence the outcomes of the matching process. The goal is to create stable matches where no pair would prefer to be with each other over their current matches. One of the most famous applications of Matching Theory is the Gale-Shapley algorithm, which was developed to solve the stable marriage problem. This algorithm ensures that participants are matched in a way that no two individuals would rather be with each other than their current partners, leading to stable and efficient outcomes in various matching scenarios.