Cleopatra arrives in Rome to pay her respects to Caesar--and to attempt to get her young son legitimized. The Egyptian Queen's arrival intrigues Mark Antony and rankles Atia, who barely tolerates her new rival and Servilia during a fete. Called off a grisly mission at the last minute, Timon returns home to find his brother Levi has unexpectedly arrived from Jerusalem, his disdain for all things Roman intact. Meanwhile, Erastes' death has plunged the Aventine Collegium, and Rome's river commerce, into chaos. In an effort to restore order, Mark Antony orders Vorenus to assume Erastes' captaincy, and he and Pullo bully the warring gangs into an uneasy truce. Frustrated by Mark Antony in his attempt to secure his inheritance, Octavian takes out a loan to pay off Caesar's promise to the people, angering his mother and especially Mark Antony, who refuses the boy's offer of a power-sharing strategic alliance. The confrontation leads to Octavian leaving Rome.

Octavian changed his name to Augustus to "soft up" the senate's objection when he tried to take Caesar's place. Augustus and Anthony team-up against Brutus and won.

Later on, Augustus turned against Anthony and Cleopatra (they're lover) for sole control of Roman Empire and Augustus won. Augustus embarrassed Cleopatra by parade her in Rome public in chain that lead her suicide. I don't know what happened to Anthony.

Augustus became the most popular Emperor in Rome history.

I might not making sense… you will have to look up in Google that usually have tons of information.

Marc Antony fell in love with Cleopatra; the two had twins (and another child) and eventually moved to Alexandria.

Skipping ahead (a LOT of stuff happened between then and what eventually happened), Rome and Augustus eventually declared war on Egypt. At the Battle of Actium, Antony's quickly-assembled navy was crushed by Rome. There were rumors that a) Augustus was going to capture Cleopatra and parade her in chains through the streets of Rome; and b) that because of this, Cleopatra had committed suicide. Neither of these were true (at the time), but Antony believed the stories and committed suicide (seppuku-style) on the battlefield. Cleopatra died a few days later, allegedly by allowing two asps to bite her.

Augustus outlived them both by almost 45 years, dying in Rome of natural causes in 14AD.