(The picture on the left are students standing on the old sacred placed in front of the Senate building.)
Roman government from its founding to its fall was a mix of democracy and a republic. It changed from a monarchy, to republic based on combination of obligarchy and democracy.
500 BC was the time the Roman Republic was first set up. Consuls who were the two men in charged at that time and women weren't permitted to be consuls. Consuls controlled the army, and the consuls also decided if they wanted to start a war and what the laws were and how much tax they wanted to collect. Both of the consuls had to agree in order to change anything. If one of the consuls said "veto" (I forbid it), then nothing would be done.
Advice from the Senate were given to the consuls, if they needed it. Senates were made up of wealthy men in Rome. Again, women weren't allowed in the Senate, either. If you got in the Senate, you will have to stay there for the rest of your life. Eventually, consuls will join the Senate, and most of the senators were from families where their grandfathers or fathers had been in the Senate. Consuls usually did what the Senate advised.
Prefects in Rome, were to run the city. Some of the prefects heard court cases, some ran meat markers or vegetable markets or the port.
Tribunes spoke for the poorer people in the Senate. They are elected by the Assembly. Tribunes could forbid anything that the Senate voted on that affected the poor people. And again, the tribunes were all men.
Assembly was made up of men who were free and grown, and had an Roman citizenship. They voted on few big issues, if the consuls asked them to. The elected consuls, prefects, and also the Senators. The Assembly was formed so richer citizens got more votes that the poorer citizens.
When Romans began conquering other places which were far away from Rome, they had a system of provincial governer. They were men who took charge of the province of the Empire, and also who heard court cases there. They also took charge of the army while it was conquering places.
Around 50 BC, the time of Juilius Caesar, the generals began to take over government and they didn't pay any attention to the consuls or the Senate anymore, and just do as they pleased. The generals could do that since they had the whole army with them.
In 31 BC, Augustus was one of these generals, but he realized that people didn't like pushing people around, so he decided to set up a new system, a system where he had all the power. He kept the Senate, and the consuls, and Augustus said they were in charge, but he made the Sente voted to give him the powers of a tribune for life so Augustus could forbid anything the Senate tried to do that Augustus didn't want them to do. Also, Augustus kept control of most of te army, that way he could kill anyone who got in his way.
The system with the Senate and consuls, but Emperors had all the real power kept going for the next 1500 years.