The art of descending into a location on a single (occasionally double) rope. You will want (but not require) a rope (preferably static for rappelling, dynamic if you are lead climbing on this rope also), a harness, a carabiner, and a descender (probably a figure of eight, or the safer rescue 8, which has ears to keep the rope from getting caught). An abseil is used when you plan on ascending the rope or have a means of getting back to where you started. See also rappel and prusik
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The above seams more climber focused. Its more normal with the underground to use caving SRT equipment. Decent is most likely to be a Petzl STOP or a rack, using an SRT harness as opposed to a climbers harness then a croll and hand jammer to prussic backup the rope. Climbing equipment is not best suited for a lot of underground rope related work. A figure 8 is totally avoided in caving as in a free hang it will induce spin.