To elaborate, were there specific training programmes for gymnasiums, did they have standard weightlifting exercises and so on?
Most Greek city states had a tradition of their male citizens/nobility participating in various sports (the track and field sports/wrestling/boxing and martial arts) which also included javelin throwing. Gymnasiums were also very important in a young man's life where weight lifting and gymnastics were practiced.
As for Sparta they had the "Agoge" which was formalized military training/war on the slave class. Google Agoge if you want more info on that.