Lieutenant Maxwell Burke was a Starfleet officer who lived in the latter half of 24th century. He served aboard the USS Equinox as first officer, under the command of Captain Rudolph Ransom during the 2370s. (VOY: "Equinox")
Burke attended Starfleet Academy in the 2360s, along with fellow cadet B'Elanna Torres, with whom he was romantically involved and affectionately nicknamed "BLT". During their time together, Burke expressed to B'Elanna his contemplation of resigning, although he ultimately chose to remain and pursue his commission.
By 2371, Burke had been assigned to the Nova-class science vessel Equinox. In that year, the Equinox was forcibly transported to the Delta Quadrant by the alien entity known only as the Caretaker. (VOY: "Equinox")
The Delta Quadrant
During their time in the Delta Quadrant, the Equinox crew found that they were ill-equipped to deal with the dangers of the region. After five years, over half of the crew was dead, their food reserves were at a minimum, and their dilithium was all but gone. In an attempt to return to the Alpha Quadrant, the crew began engaging in criminal experiments to augment their warp drive, wherein they began murdering nucleogenic lifeforms and converting their remains into a crystalline compound which acted as a source of fuel, providing them with the opportunity to return to Earth in a matter of months.
In 2375, the Equinox crew encountered the USS Voyager, another Starfleet vessel which had been stranded in the Delta Quadrant by the Caretaker, and Burke was reunited with his old girlfriend, B'Elanna Torres, who was serving as Voyager's chief engineer. The Voyager crew assisted in making repairs to the Equinox, and in fending off attacks by the nucleogenic lifeforms, which were attempting to destroy the ship in retaliation for the Equinox crew's actions. Burke and the rest of the crew initially attempted to conceal their actions against the lifeforms from the Voyager crew, but they were eventually discovered and confined by Captain Janeway. Escaping, they were able to steal Voyager's field generator, which had been modified to confine the lifeforms, and left Voyager to be attacked as they resumed course towards the Alpha Quadrant. (VOY: "Equinox")
Eventually, Captain Ransom decided to halt the experiments and surrender to Captain Janeway, leading Burke and a small group of Equinox crewmembers to mutiny and take control of the ship. Ordering Ransom confined, Burke took command and attempted to destroy Voyager, but was thwarted when Ransom and Ensign Marla Gilmore managed to beam the rest of the crew off of the ship. As the Equinox faced destruction by the aliens, Ransom revealed his actions and pleaded Burke to evacuate to Voyager, but he refused. Burke and the remaining crewmembers attempted to reach the ship's only remaining shuttlecraft, but was ultimately killed on the way to the shuttlebay. (VOY: "Equinox, Part II")