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Abstract: No enemy can match a friend. Jonathan Swift Introduction Many economic problems concern the need to match members of one group of agents with one or more members of a second group. For example, workers need to be matched with firms, graduate students with graduate schools, authors with publishers, landlords with tenants, and men with women, to name just a few. Matching problems pose three central issues: Is there a stable matching – one that cannot be upset by individual negotiations? What procedures or institutions accomplish stable matchings? Are these procedures manipulable? This chapter gives a brief introduction to the economics of two-sided matching. To keep matters as simple as possible, we focus on one particular class of matching problems: the matching of two distinct groups (two-sided matching). Notation and Basic Assumptions Consider the problem of matching two distinct groups, say W := { w 1 , …, w n } and M := { m 1 , …, m n }, metaphorically referred to as the marriage problem . Keeping the particular application of marriage in mind, W may be remembered as the group of women and M as the group of men . Each man is assumed to have a complete and transitive strict preference defined on W , and each woman has such a preference defined on M . These are conveniently described by a preference matrix , as in the following example. Example 7.1 The preference matrix below gives the rankings of three men and three women.