What is the inital for the degree that law schools confer on graduates?

J.D. (juris doctor) is the primary one. There is also an LLM (master of laws), which is a degree for someone who already has a law degree. This is either for a foreign attorney seeking a legal degree in the U.S., or for an area of specialty for an American lawyer (such as an LLM in tax law). There are even more advanced degrees such as the LLCM (Master of Comparative Laws) and SJD (Doctor of Juridical Science), but these are rather rare.