  Let $q$ be a nontrivial odd prime power, and let $n \ge 2$ be a natural
number with $(n,q) \ne (2,3)$. We characterize the groups $PSL_n(q)$ and
$PSU_n(q)$ by their $2$-fusion systems. This contributes to a programme of
Aschbacher aiming at a simplified proof of the classification of finite simple
groups.
