The research area "Design of Matching Markets" focuses on the analysis and design of markets in which the use of money is impossible or undesirable. Prominent examples include the allocation of school and university places or the distribution of donor organs. Furthermore, there are markets in which participants do exchange money, but at the same time, the emergence of market prices is prevented by other restrictions. The market price is relevant for efficiently managing the allocation, as is the case in labour markets. A major challenge in these markets is to design the allocation mechanism in a way that all participants have an incentive to reveal their true preferences. This can prevent individual participants from taking advantage of others by proceeding strategically reporting their preferences. It is also important to achieve stable and efficient allocations given the preferences of the market participants.