Sector 001 or Sol Sector is the central sector of space of the United Federation of Planets in which the Sol system is located. (TNG: "The Best of Both Worlds", DS9: "Emissary")
Data examined the Starbase ops status of the Sol Sector in late 2364, finding proof for a conspiracy amongst the highest ranks of Starfleet Command. (TNG: "Conspiracy")
In 2371, a microscopic singularity passed through Sector 001 and exploded. This created the conditions for an accident that sent Benjamin Sisko, Jadzia Dax and Julian Bashir back in time to the year 2024. (DS9: "Past Tense, Part I")
In 2372, Julian Bashir gave Nog a PADD containing a guide for life on Earth as a going-away present. (DS9: "Little Green Men")
The letter "a" in "Earth" on the PADD was substituted with the Starfleet Academy logo. The Battle of Sector 001 between the Federation and the Borg occurred in this sector in 2373. (Star Trek: First Contact)
In 2407 The 52nd Fleet, under the command of Admiral Robert LoDona, assigned Task Force 19 to attack and breach the Mars Defense Perimeter. This battle was the final push by the 52nd Fleet to finally restore the United Federation of Planets to it's previous government, usurped by Rodrigo Doenitz.
Task Force 19 was successful in breeching the MDP, after capturing Starbase Valhalla. The 52nd Fleet, won the battle of sector 001, but at great cost.