The Romans set up a Republic after overthrowing their tyrant King (Lucius Tarquinius Superbus) around 498 to 496.
Lucius Tarquinius Superbus shortened to 'Tarquin' took over the throne in Rome by murdering family members and assassinating the former king. At this time it was common for rulers to be replaced by assassination.
Tarquin immediately put to death all the Roman Senators who opposed him or were suspected of sympathizing with others. Tarquin then began a series of battles to take over wealthy towns and civilizations next to Rome to enhance his kingdom and wealth that he used to build lavish architectures like the Temple of Jupiter Optimus Maximus.
Finally the Romans became tired of the continuous building and battles, and the populace were ready to expel the King. The final push came from Lucius Junius Brutus who led the people to revoke the mandate of the king. After a couple of vicious battles, Tarquin was defeated and the Roman republic commenced.
A republic is characterized by a government that is for the people as opposed to a kingdom that favors the desires of one person or family.