Prydonian Academy

The Prydonian Academy was an educational institution on Gallifrey. Its pupils wore scarlet robes, and were Time Lords by virtue of biology, not education. Amongst other things, the Academy taught them how to instantly calculate "complex temporal induction problems". It had a fortress-like appearance and a population segmented by ability; only a select few were brought to its highest towers to be taught "darker things". (PROSE: Timewyrm: Revelation)

Physically, it was situated at the base Mount Cadon, Gallifrey's highest peak. An imposing structure, it was a dark, ebony building (PROSE: Revelation (novel), Lucifer Rising) at the northern border of "southern Gallifrey". (Lucifer Rising)

As Lord President, the Doctor was able to access its so-called "black collection" and steal a portable temporal link. (Revelation)

On one occasion, the Doctor claimed to have attended the Prydonian Academy with the Master, though the Doctor equivocated on the point. (PROSE: First Frontier)

Behind the scenes

Since "the Academy" typically means the "Time Lord Academy" in works like Interference - Book One and the Gallifrey audio series, and since Paul Cornell barely mentioned the place in Revelation, it's unclear whether the Prydonian Academy is a formal name for the Time Lord Academy, a part of a larger whole, or, indeed, what exactly it is. It was also unclear whether the Prydonian Academy was uniquely attached to the Prydonian Chapter in some way, because Cornell never specified any such connection.