In this chapter, weMatching markets will study two-sided matching between two groups of individuals or objects under nontransferable utilities. Section 17.1 will introduce a one-to-one matching environment, known as the marriage market involving a set of men and a set of women, and present several results about stable matchings in this environment. Section 17.2 will extend some of these results to a many-to-one matching environment involving a set of institutions and a set of individuals. In this environment, a many-to-one matching assigns each institution to a distinct group of individuals. Finally, Sect. 17.3 will study a particular one-to-one matching problem, known as the housing market, where the aim is to find a stable matching that reallocates the houses of a finite number of individuals among them.