1. to put down (In the sense of putting an object down on the ground. Usually for somewhat heavy objects, so it would sound a bit weird for putting a glas on a table. "hinstellen" is the better choice there.)
2. to turn off, to disconnect, to cut off (Mainly used in context of housing utilities being turned off by the supplier, and also engines. And for bad habits. It does NOT sound good for lights or small devices.)
Opposite (closest): anstellen
3. to base one's argument on ("abstellen auf+Acc" - a very stiff phrasing that you barely ever hear in daily life.)
