The Academy allows the player to train the one elite infantry unit: the Hoplite, which is upgraded to Phalanx, and then Centurion. They are fairly expensive, but worth their cost as they form a solid core with which to assault an enemy settlement.
Researching Architecture in the Government Center increases hit points and decreases construction time. The Academy is available from Bronze Age onwards. Persians are the only civilization that cannot build an Academy and cannot train units from the Academy.
The Academy was the Greek equivalent of a school. Students, usually only free men and favored slaves, received an education at the Academy. Subjects of study included the typical fare of schools, but also politics, athletics, and military training.
The most rigorous of the Greek Academies were those of Sparta where boys were taken from their parents at an early age and educated in a military environment. The Academy prepared the individual for service to the state as a citizen and a soldier in the phalanx. In one of the remarkable encounters of history, the future Alexander the Great was educated at the Academy of Aristotle.