Kōan (公案) is a legal term. It means "public case" - a case on the record, the way a court keeps precedents. Zen borrowed the word for these: short, odd exchanges between a teacher and a student, collected and studied like case law. Most of them don't make sense, and a lot of them are funny, but they're supposed to be: a kōan is built to jam the part of your head that goes looking for the answer.
Each entry has three parts: the original, a translation, and a pointer. The pointer is the useful bit. It won't solve anything, but it gives you what you'd need to get the joke: who these people are, and where the trap is set. The originals are public domain; the translations are free to use.
How it works
A taste — the most famous case in the book:
1Zhaozhou's Dog趙州狗子
趙州和尚因僧問。狗子還有佛性。也無。州云無。
A monk asked Zhaozhou, "Does a dog have buddha-nature, or not?" Zhaozhou said, "Wú."
Sayings of Linji Yixuan (臨濟義玄, d. 866), compiled by his disciple Sansheng Huiran (三聖慧然); standard recension edited by Yuanjue Zongyan (圓覺宗演), 1120 · compiled 9th c.; recension 1120 · 66 cases · 66 translated so far
Sayings of Zhaozhou Congshen (趙州從諗, 778–897); transmitted within 古尊宿語錄, compiled by the Song monk Zezangzhu (賾藏主) · sayings 9th c.; Song anthology · 46 cases · 46 translated so far