The Greek culture began before the Roman. The Iliad, one of the earliest of the great written Greek works, appeared roughly 700 years before the Aeneid , an early Roman work. The Iliad in turn was based on a good 300 years of verbal story telling.
Greek civilization was mostly conducted from small city states. The Greeks loved life and lived it with zest. They had little interest in the afterlife which, even for the greatest of men, was believed to be an eternal unpleasantness. In the Odyssey , the dead Achilles says that he would rather be a slave in life than king of the dead. The best that a man could hope to do would be to perform great deeds that would be remembered after his death. Because they highly regarded intellectuals (poets, philosophers and others) in addition to their great warriors, great deeds could be accomplished by all.
The Greeks believed in individualism and prized differences in personality and character. They were fascinated by the contradiction that it is those very virtues that made a man great which can lead to his undoing. This is very subtle thinking.
Their myths and religion reflect these traits. Their gods were personalized with individual strengths and flaws; gods made mistakes, got embarrassed and were caught cheating on their spouses. But, also there were gods who were heroic, wise, loving, and developed essential crafts like weaving.
Mortal heroes also played an important role in the myths. There were times when the gods needed a mortal hero to win battles for them. But very rarely did a hero become a god. Many of the most heroic tales involve snatching someone back from the underworld. This is in stark contrast to those religions in which getting to the next world the right way is the main goal.