Rome was not born a republic. For its first two and a half centuries it was ruled by kings, and the memory of that monarchy shaped everything the Republic later became.
The last king
Tradition dates the change to 509 BC and pins it on one man: Lucius Tarquinius Superbus, "Tarquin the Proud," a king remembered as arrogant and violent. The final outrage, the Romans said, was the assault of his son on Lucretia, a noblewoman whose suicide became a rallying cry. Led by Lucius Junius Brutus, the aristocracy drove the royal family out and swore never to be ruled by a king again.
Res publica
In place of the king they built a res publica: literally "the public thing," the commonwealth. Power that had belonged to one man was split up, shared out, and hedged with limits. Two annually elected magistrates, the consuls, took the king's executive authority, but there were two of them and they served for only a year, so no one could turn office into a throne.
The fear of kingship
That fear of monarchy never left Roman politics. Centuries later, calling a rival a would-be king was among the deadliest accusations one could make, and the memory of Brutus expelling the Tarquins was invoked again and again. When Julius Caesar was assassinated in 44 BC, one of the conspirators was another Brutus who consciously cast himself as the heir to that founding act.
A system, not a plan
The Republic was not designed all at once. It grew by accretion (offices added, rules adjusted, crises patched over) until it became a dense web of magistrates, councils, and customs with no written constitution at all. Its stability came not from a document but from mos maiorum, "the way of the ancestors," a shared sense of how things were properly done. That unwritten tradition held Rome together for a remarkably long time, and its slow unravelling is the story of the Republic's fall.