The Roman empires origin date can be traced back to the 8th century BC, The original people of Italy was the latins. Then they advanced into a city state instead of random small villages. Then the first Roman rebublic was born after they over threw the seventh king of Rome: Tarquinius Superbus in 509 BC. After this the Romans would beginning to conquer the rest of Italy and North Africa through the Punic Wars. And then they went on to conquer France, Iberia, Greece, Turkey, Israel, Eygpt, Armenia, and England, making them the strongest European power of Classical Age.
The Fall of the Roman Empire wasn't really the fall of the whole empire, it was only the fall of the Western Empire because at this point it had been split into 2 parts: The west and east empires. Through the mix of an incompetent 14 year old emperor, lack of military might and lack of funding the Western Roman Empire fell to Goths in 476AD spliting the west into the Ostrogothic and Visigothic kingdoms.
146 years, 3 months and 24 days before the fall of the western empire the Byzantine Empire was formed from the Eastern Roman Empire. Since Rome wasn't in the empire anymore they had to call it something diiferent. With the eastern capital of Constantinople secure of barbarian attacks the Emporer Justinian took back Rome in his Reconquest of the Western Empire in 551AD.