The Battle of Axanar was a battle fought by the Federation at Axanar, led by Fleet Captain Garth of Izar.
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 he and Spock to work together as brothers. (TOS: "Whom Gods Destroy")
As stated in the Star Trek Encyclopedia (1st ed., pg. 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." The non-canon FASA source book The Four Years War claims the battle was between the Federation and the Klingons.