(covers information from several alternate timelines)
This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
The Vulcan Science Academy (VSA) was an advanced educational and research institute located on Vulcan. After reunification with the Romulans, it became known as the Ni'Var Science Institute. (DIS: "Unification III")
Michael Burnham was the first Human to attend the Vulcan Science Academy, from 2245 to 2249, where she studied quantum mechanics. (DIS: "The Vulcan Hello", "The Butcher's Knife Cares Not for the Lamb's Cry")
As late as 2249 of the alternate reality, no Vulcan in the Academy's entire history had ever declined admission. But, as in the prime universe, Spock declined acceptance in protest to the admission council's labeling his Human mother a "disadvantage". The Academy would be destroyed, along with all of Vulcan, in 2258. (Star Trek)
In 2250, Spock decided to join Starfleet rather than attend the Vulcan Science Academy, against the wishes of his father, Sarek. Spock's decision was motivated by the realization that he would never be seen as an equal by the staff, only as someone who had "overcome the handicap" of half-Human parentage. (TOS: "Journey to Babel")
Following the Federation-Klingon War peace accord in 2257, the Vulcan Science Academy offered Paul Stamets a permanent teaching position, which Stamets accepted. (DIS: "Brother") Stamets, however, ultimately passed up the position. (DIS: "Such Sweet Sorrow")
By the mid-22nd century, the Vulcan Science Academy had spent a deal of time studying sub-quantum transporting but had little success. Earth's expert on transporters, Emory Erickson, had been trying to get his hands on some of the Science Academy's research for years to no avail. Erickson later claimed that it was probably just as well, as it might have sent him down the wrong path. (ENT: "Daedalus")
Prior to the sealing of the ruins in the mid-23rd century, the VSA excavated archeological sites on Tagus III. The Jacobson Excavation recovered artifacts from the Post-Ramirez Era and Sepulveda Period. (TNG: "Qpid")
The novelization of Star Trek suggests that, after declining acceptance, Spock salutes the council with a "distinctly Human digital gesture" unfamiliar to them – a raised middle finger – before walking out.