The book gathers some of the most important theories of matching, and guides the reader to the discovery of the practice of Market Design. The field of Matching Theory is devoted to study and solve allocation problems into matching markets, where prices and payments cannot be used, and agents’ preferences are the discriminants. The assignments' solutions lie at the crossing of Economics, Mathematics and Computational Science, and consist of mechanisms that have the strength to be tailored and implemented into real-world contexts. The economist becomes an engineer who uses theoretical tools for designing, and practically building, efficient markets for bettering the well-being of all the agents involved. The book shows that in Economics there is more than banks, money and profit, and honors the research work for which L. S. Shapley and A. E. Roth were awarded the Nobel Prize for Economic Sciences in 2012. It is suggested to anyone who wants to discover how Economics can serve the community welfare.