The classification of finite simple groups

This theorem describes completely all finite simple groups: A finite simple group is either cyclic groups of prime order, alternating groups, groups of Lie type (included some twisted families), or one of 26 sporadic simple group. The proof extends over many paper by many people. The completion of the project was announced in 1983, but some incomplete part was replaced by a complete proof only more recently. There was a project for major revised and simplified proof but it was also very hard. Here is a link to a review paper of Solomon. (The answer was suggested by Victor Protsak.)