Octavian was a very successful leader in the Mediterranean. He had safeguarded trade by wiping out the pirates who captured Egyptian grainships headed for Rome. Mark Antony, however lost several campaigns against the Parthians. Soon after, he fell in love with Queen Cleopatra of Egypt. Cleopatra was Caesar's former love. Antony was married to Octavian's sister, Octavia, to strengthen his political power, but divorced her to marry Cleopatra. Octavian was furious at the insult to his family. He was even more furious when Antony announced that Cleopatra's son, Caesarion, was Caesars legitamate child. Antony was implying that Octavian had no legal right to Caesar's name and inheritance. Antony left Rome and went to live with Cleopatra in Rome. Romans thought Egypt was corrupt and superstitious. Octavian wanted to restore old Roman virtues of a good government and plain living. Octavian was worried that Antony was trying to control Rome from Egypt, so on September 3, 31 BC, both Octavian's, and Antony's fleets met near Actium, Greece. Antony's fleet was bigger, and had many more weapons that Octavian. Despite his smaller army, however, Octavian won the fight. He won because in the midst of the battle, Cleopatra started to sail away and Antony abandoned his fleet and sailed after her. Two hours later, Octavian won the battle. Eventually, both Mark Antony and Queen Cleopatra committed suicide, and Caesarion was executed. Octavian was now the undisputed master of the Roman world.
This is a statue of Octavian
This is a statue of Mark Antony

This is the Battle at Actium where Octavian won the war over Mark Antony

Greenblatt, Mirium. Augustus and Imperial Rome. New York: Benchmark Books, 2000. Print.