The Sith Academy on Korriban was a facility in use during the Jedi Civil War, dedicated to training Force sensitives in the Dark Jedi arts to later become Masters, and running archeological projects in the Valley of the Dark Lords.
The exact time of establishment of the academy is unclear, though it was probably founded sometime during the Great Sith War and was in full operation as of 3,993 BBY.
Revan and Malak used the academy upon their return as Sith Lords to train Dark Jedi for their empire. Its students during this time were either Force sensitives looking to take a side in the Jedi Civil War, or fallen Jedi, disillusioned with either the Jedi, the war or the Republic in general.
Whether an initial founder or former student, Jorak Uln was an early headmaster of the academy. In later years this passed to Uthar Wynn as he overthrew the former master in the manner of the Sith. Upon Revan's return to the planet during his search for the Star Maps, Uthar Wynn was killed in line with his apprentice, as Yuthura Ban intended. After Uthar´s death, Yuthura left the academy to rejoin the Jedi. However, the redemption of Yuthura and the death of Uthar merely began the incident known as the Skirmish on Korriban. When leaving the valley, Revan and his crew were interrogated by the Sith Guards about why he left alone. In this, he accidentally gave himself away. The resulting battle pitted the entirety of the Academy against the crew of the Ebon Hawk. However, due to the experience and training that the crew had, added to the sheer power and fighting prowess of the former Dark Lord, they managed to defeat the Sith and escape, but in doing so killed most if not all of the Sith at the academy.
It was apparently repopulated after this and before the end of the war.
The academy's history all but ended with the climax of the Jedi Civil War. Shortly after the destruction of the Star Forge, infighting at the academy turned Korriban into a graveyard once more. It was looted after the First Battle of Korriban.
The Jedi Exile came to Korriban to search for Jedi Master Lonna Vash. The Exile was encountered by an academy totally different than Revan did during his Star Forge quest: the academy was completely automated, computers replacing flesh-and-blood Sith teachers. As she wandered the emptied academy, encountering only tuk'ata and Sith Assassins that chased her. She found the Jedi Master's corpse inside the interrogation room. On her way out, she briefly dueled with Darth Sion. However, at the urging of Kreiawho preferred not to accompany the Exile and thus stayed on the Ebon Hawkshe fled the battle, knowing she would have another chance to battle the Sith Lord.
It was reopened during the New Sith Wars following the Battle of Korriban, and a young Darth Bane trained there. At that time, it along with most of the other major 'historical' sights had been pillaged by the Jedi in their attempt to destroy all remaining vestiges of Sith lore. Due to their efforts, the academy's formerly prestigous archives were now forced to rely on haphazardly arranged books and manuscripts, which were practically ignored by Kaan's Brotherhood of the Sith.
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Picture taken by me.