Unicorn
A unicorn, represented by u, is a type of monster that appears in the dungeon starting at mid-game. They are very fast and tend to prance around, which often makes them difficult targets. They can also deal surprising amounts of damage.
There are three types of unicorns: white, grey, and black, which correspond to lawful, neutral, and chaotic alignments respectively. The unicorn of your alignment will be peaceful; all others will be hostile. Unicorns in bones files or created by polymorph traps may be exceptions to this rule, but killing a unicorn of your own alignment always carries a -5 Luck penalty. (As is usual in NetHack, this penalty will not apply if you encourage your pet to kill it.)
When killed, a unicorn leaves a unicorn horn with its corpse. Eating a unicorn corpse has a chance of giving poison resistance.
Sacrificing a unicorn at an altar is a special case and is covered in the page on altars. Basically to receive alignment and luck benefits you should sacrifice a unicorn of a different alignment than you at your own altar.
Throwing gems to a unicorn of your alignment can bring luck increases as well as assist in identification. If the unicorn "graciously" accepts your gift it is worthless glass. If he "gratefully" accepts your gift it is a valuable gem.
Throwing gems to a hostile unicorn will calm him down. If the gem is worthless glass, there will be no effect on your Luck, but if it is real and the unicorn is not of your alignment, your Luck may go up or down.
