Garth's tactics and actions in this battle were required reading at Starfleet Academy. It was noted by James T. Kirk that Garth's victory was instrumental in making it possible for him and Spock to work together as brothers. (TOS: "Whom Gods Destroy")
Background information Edit
As stated in the Star Trek Encyclopedia (1st ed., p. 18), "it was not established who the opponent was in Garth's victory. It has been speculated that it might have been the Romulans, although the history implied by TOS: "Balance of Terror" indicates that there was no Federation contacts with the Romulans during that time frame." Additionally, based on Kirk's comments, "the Axanar battle apparently had something to do with holding the Federation together."
According to the FASA sourcebook The Four Years War, the battle was fought between a Federation fleet lead by Garth of Izar commanding the USS Xenophon and a Klingon invasion force leg by Admiral Kkorhetza zantai-Riskai. It became the start of conflict known as the Four Years War.
According to the novel Garth of Izar, the battle was fought between the USS Heisenberg commanded by Garth of Izar and a single Klingon warship. It occurred in 2251.
According to the book Star Trek: The Original Series - Core Game Book the Axanar Rebellion was a conflict between the Federation and the Axanari. The Axanari were offended by the suggestion that their application for Federation membership should be rejected because of their inferior starships. They responded by conquering several planets and presenting them to the Federation. The Federation demanded that the Axanari immediately withdraw from their conquered planets which angered them even more. Garth of Izar commanded the USS Constitution during the conflict and the Federation was able to win despite the Axanari fleet being numerically superior.
According to the book Star Trek: Federation - The First 150 Years the battle was fought between the USS Constitution, commanded by Garth of Izar and three Klingon warships.