|Affiliation:||United Federation of Planets|
In 2293, the location of Memory Alpha in the Milky Way Galaxy was labeled in a star chart that was in Captain James T. Kirk's quarters aboard the USS Enterprise-A. (Star Trek VI: The Undiscovered Country, okudagram)
In the early-to-mid 23rd century, the Federation built a central library on an unnamed planetoid. The library would hold the total cultural history and scientific knowledge of all planetary Federation members. During assembly, the library wasn't installed with protective shields as this was considered inappropriate for a facility dedicated to academic research.
As of 2269, the library complex was an array consisting of five large and seven smaller domes on the surface of the planetoid. Aside from the technicians, the occupants of Memory Alpha varied with the number of scholars, researchers, and scientists from various Federation planets who were using the computer complex at any given time.
In that year, the USS Enterprise was en route to transfer newly-designed equipment to Memory Alpha. Lieutenant Mira Romaine was on her first deep space assignment to supervise the transport from the emergency manual monitor. Before the arrival of the Enterprise, Memory Alpha was attacked by the non-corporeal Zetarians.
While the Zetarians were attempting to take over the bodies of the personnel of Memory Alpha, they managed to cause extensive damage to the complex. The memory core of the computer, called the central brain, was burned out. The energy generator was rendered inoperative. All occupants of the complex died from brain damage caused by resisting the mind control efforts of the Zetarians. After the Zetarians were destroyed, the Enterprise returned to Memory Alpha to begin repairs. (TOS: "The Lights of Zetar")
According to Michael Okuda: "Based on the size and spacing of the windows, I'd estimate that each of the domes must be similar to the Superdome." also "If you look very closely at the far left dome, you might notice a small blue patch on the top of the dome. That's the Memory Alpha emblem." 
According to Star Trek Maps (p. 27 & chart D), Memory Alpha was established for the Federation Centennial celebration and opened to the general public two years later. The library computer was only partially destroyed by the Zetarians and was overhauled after the attack. The resident population was six hundred. Memory Alpha had a small moon called Arsende. According to Star Trek: Star Charts ("United Federation of Planets I"), Memory Alpha was located in the Alpha Quadrant.
The Memory Alpha facility is mentioned in the 1988 novel sequel to "The Lights of Zetar", Memory Prime. Memory Alpha is also referred to in Boogeymen, and research done at the complex was referenced in Demons of Air and Darkness and Captain's Blood. Memory Alpha is mentioned in Losing the Peace.
By 2409, in the game Star Trek Online, the complex expanded to circumnavigate the planetoid. The facility functions as a hub for crafting in the game, used to fabricate more advanced versions of standard items (equipment, weapons and such) as well as data sample storage. Memory Alpha is in the Alpha Centauri sector block, near the Romulan Neutral Zone.