Strategic decision-making refers to identifying the best way to achieve goals and objectives, maximizing systems performance or social welfare. The problem of matching demand and goods is an important problem in society, some examples are: student placement in schools, organ donation, where patients are matched to potential donors, and labor markets. Recently, “matching and market design” has received ever increasing interest from many research areas to solve the resources allocation problems, i. e., the challenging problem of properly assign resources to machines. This course introduces the theory of matching and market design, presents theoretical fundamentals of matching games, and discusses how the theory can be applied to different applications and scenarios, investigating the main classes of matching games. The emphasis will be put on recent advances in the topic and open questions will be presented so that interested students can promptly come to the frontier and begin their own research.