Judge Advocate General

From Memory Alpha, the free Star Trek reference

A Judge Advocate General (often shortened to JAG) within Starfleet is an officer who advises Starfleet on and administers courts martial, as well as oversees other Starfleet legal matters and personnel. Legal counsel within Starfleet report into the senior JAG officer as part of the department known as the Judge Advocate General's Office (or simply the "Judge Advocate's Office").

Areel Shaw was a JAG officer assigned to Starbase 11 in 2267. While there she prosecuted the court martial of Captain James T. Kirk on the charge of culpable negligence. (TOS: "Court Martial")

Phillipa Louvois was also a member of the Judge Advocate General's Office. In 2355 she presided over the investigation into the loss of the USS Stargazer. In 2365, as a captain, she was the commander of the JAG office of Sector 23. One of Captain Louvois' first rulings in 2365 was that Lieutenant Commander Data was not the property of Starfleet. (TNG: "The Measure Of A Man")

The Judge Advocate General's Office was responsible for the investigation into the mutiny that occurred aboard the USS Pegasus in 2358. (TNG: "The Pegasus")

Rear Admiral Bennett was the JAG officer in 2373 who ruled on Richard Bashir's criminal actions when he plead guilty to the resequencing of his son Julian's DNA. (DS9: "Doctor Bashir, I Presume")

Why Richard Bashir, a civilian, would be prosecuted by the JAG office of Starfleet, a paramilitary organization, was never explained, although as part of the elder Bashir's plea agreement, Julian was allowed to continue to serve in Starfleet.

Non-Starfleet persons, including non-Federation citizens, can lodge formal complaints with the JAG that arise from actions taken by Starfleet personnel. (TNG: "Gambit, Part II")

The branches of Starfleet
United Earth: Command • Materiel Supply Command • Medical • Mission Control • Security • Section 31 • Training Command
United Federation of Planets: Administration • Administrative Operations • Advanced Technologies • Command • Communications • Control • Dental • Engineering Corps • Exploratory Division • Information • Inspector General • Intelligence • Internal Affairs • Judge Advocate General • Materiel Supply Command • Medical • Mission Operations • Operational Support Services • Operations • Orbital Operations • OSHC • Research and Development • Science • Section 31 • Security • Shipyards Operations • Stellar Imaging • Tactical • Training Command • Warp Technologies