We analyze sorting in a standard market environment with search frictions and random search, where both workers and jobs have multi-dimensional characteristics. We offer definitions of multi-dimensional assortative matching in this frictional environment. We say that matching is positive assortative in dimension (j; k) if workers with higher endowments in skill dimension k are matched to a distribution of jobs with higher values of job attribute j, in the sense of first-order stochastic dominance. We derive three main insights: First, the key condition for positive sorting is a single-crossing property of the technology. Second, there are significant sorting trade-offs, whereby positive sorting arises between a job attribute and skill with relatively strong complementarity in production, while negative sorting arises in the dimension in which complementarities are weaker. Third, sorting is based on comparative advantage, whereby workers with uniformly higher skills do not sort into jobs with uniformly higher skill requirements but instead into jobs that suit their skill mix.