Do you mean Aristotle's Lyceum? Or do you mean the Academy? The Academy was not a building, it was a grove sacred to Academus, north of the city. The site is quite large, with a number of buildings, most of which were built during the Hellenistic Period. The Lyceum, where the Peripatetics met, was also originally a sanctuary to Apollo and technically described the entire space, not just the gymnasium built there in the 5th Century. Like the Academy, the Lyceum was not a single building, but a number of them, the most important of which is the gymnasium, although Aristotle generally taught on the various walkways (περίπατοι) scattered throughout the sanctuary, from which the school got its name--the archaeological site was opened to the public a few years ago