There are several different, and somewhat incompatible, mythic traditions describing the founding of Rome. It should be noted that none of this is considered historical; these different foundation myths tell us more about how Romans thought of themselves than providing a realistic account of the gradual growth of the city of Rome.
According to one foundation myth, the twins Romulus and Remus were sons of Mars the god of war, abandoned at birth and raised by wolves. When they grew up, they founded the city of Rome, named after Romulus.
A second mythological foundation story is found in Virgil's Aeneid. Aeneas is a Trojan hero, son of Anchises (a cousin of Priam) and the goddess Venus. He is commanded to flee the fall of Troy and first sails to Carthage where he meets and jilts Queen Dido and then to Italy, where he he becomes betrothed to a daughter of King Latinus and thus a progenitor of the Romans. In some accounts he is a distant ancestor of Romulus and Remus.
As we move into more historical accounts, the Etruscan King Tarquinius Superbus ruled Rome before his overthrow and the founding of the Republic in 509 BC. The Republic continued until Julius Caesar became a dictator; his successor Augustus was the first emperor. Virgil wrote the Aeneid in honor of Augustus to some degree.