An Ancient Greek gymnasium was a place where athletes trained before competing in public games like the Olympic Games. But it was more than that. It was also where men gathered to talk about the things that mattered to them. So it was also a kind of centre for learning, and was also connected with healthy lifestyle and medicine.
Gymnasia (the plural of gymnasium) were protected by the god Herakles.
The gymnasium was a large set of buildings all arranged around an open space where each type of exercise was performed. There were baths, a running track and a long colonnade around the edge where people could sit and talk while being shaded from the heat of the sun.
Because of all of this, a gymnasium was large and could often not be fitted inside the city walls.