Named after Niels Henrik Abel - Norwegian mathematician (1802-1829).
Abel is an ancient lunar crater that lies near the southeast limb 's near side. It is located to the south of the crater Barnard, at the northwest edge of the Mare Australe. The rim is heavily eroded and distorted in shape, forming a somewhat polygonal figure. It is incised and overlaid by past impacts. (wikipedia entry)
A crater is a circular depression likely created by an impact event. On the Moon they are named after deceased scientists, polar explorers, astronauts or cosmonauts.