The Romans made Greek literature and culture their own. They did this by adopting their stories in creative ways. Here are a few examples.
First, the Romans took over the Greek gods and added them to their pantheon of gods. Moreover, the Romans prided themselves on being the most pious people on earth. Cicero even says in his work,The Nature of the Gods the following words:
"If we wish to compare our [republic] to others, we will discover that in other things we are equal or inferior, but in religion, namely, the worship of the gods we are far superior."
Second, the Romans also took over Greek myths and created their own. For example, Livy is filled with pious legends.
Third, the Romans through military conquest also took over Greek learning. In fact, many of the Romans sent their children to places like Athens to study.
Fourth, the Romans also took over Greek forms of entertainment, such a plays. For example, the great Roman author, Plautus reinvented Greek comedy for a Roman audience.