Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: F. Javier Martínez de Albéniz[en] Two-sided matching markets are the main object of study of Matching theory, a branch of Game theory that involves discrete mathematics. A two-sided matching market is a market whose agents belong to one of two distinct sets and such that its outcome is an assignment of agents from one set to the other, and vice-versa. In this work, we first give some basic definitions of Game theory, and turn then to study two kinds of matching markets: one-to-one matching markets, in which an agent from one set ends up matched to at most one agent on the other set, and many-to-one matching markets, in which agents on one of the two sets might end up matched to several agents on the other set. The former will be studied by means of the marriage problem in Chapter 3, and the latter by means of the college admissions problem in Chapter 4. To conclude, in Chapter 5 there is an outline of some alternative mechanisms used in different contexts to solve problems that are similar to those already studied.