The Battle of Maxia was the unofficial name of a diplomatic incident that took place in the Maxia Zeta system in 2355, in which the Federation starship USS Stargazer, under the command of Captain Jean-Luc Picard, was attacked by a Ferengi vessel, commanded by the son of DaiMon Bok.
On stardate 40217.3 the Stargazer was on a routine survey mission near the Maxia Zeta star system. It was preparing for a full survey and sensor scan when an unidentified spacecraft was detected near one of the moons of Maxia Zeta IV. This ship later turned out to be a Ferengi vessel that may have been hiding within a deep lunar crater and was launched from said moon, though scans indicated no launch complex. All attempts to hail the ship failed.
The battle began when the Stargazer was suddenly fired upon by the Ferengi ship while traveling at warp 2 through the system. The ship was able to score two direct hits on the Stargazer. After attempts to warn the ship off had failed and with his shields nearly gone and the Ferengi closing in, Picard, with weapons coming to full charge, ordered a sensor bearing on the Ferengi ship and at the right moment, Picard devised what would later be known as the Picard Maneuver: he ordered the Stargazer to engage high warp for a split second, bringing the ship off the Ferengi's starboard bow. Since the Ferengi vessel's sensors were limited to light speed, it appeared as though the Stargazer was suddenly in two places at once.
With the Ferengi momentarily confused, they fired on the wrong ship; the one that was far away. With that, the Stargazer opened fire with a full phaser and photon torpedo barrage, destroying the attacking ship. However, the Stargazer's systems were failing, and the crew was forced to abandon ship in escape pods. The crew was later rescued, although the Stargazer herself drifted to parts unknown. The starship was eventually recovered by Bok, and used in his scheme to seek revenge against Picard, as well as to discredit the role of the "Hero of Maxia" in the Battle of Maxia with falsified logs claiming that Picard had been the one to attack the Ferengi ship without provocation. (TNG: "The Battle")
The stardate seen on the Stargazer log entry lists the date of the Battle of Maxia as stardate 40218.3; however, this would put the events of the battle at less than a year before the events of the episode. The episode clearly states the battle was nine years previous.
Found in the Picard family album, featured in Star Trek Generations, there was a certificate for the Grankite Order of Tactics, Class of Excellence, which was awarded to Jean-Luc Picard for the development of the Picard Maneuver during the Battle of Maxia. The date given for the battle was 38946.2. This certificate, however, wasn't seen in the movie.
The non-canon novel The Buried Age gives a stardate of 32217.3 for this conflict (which would be appropriate for a date nine years before the episode), as well as explaining that Bok's son was merely there to survey and claim the planet's mineral wealth for himself. The attack on the Stargazer was motivated by the Ferengis' belief that the Federation were insane for their moneyless economy. The novel also stipulates that Picard set a course for the Stargazer to fall into the atmosphere of a gas giant, but after they had left, the Ferengi vessel carrying Bok arrived and recovered the ship- which had 'ricocheted' off the gas giant's atmosphere in a slim chance-, explaining Picard's astonishment nine years later upon seeing the ship again.