Describe the transition from Roman Republic to Empire in the 1st century B.C.E.
This is a great question. There are many things that can be stated. So, here are four points.
First, during the second century B.C., Rome faced some very difficult hardships. More and more of its free citizens were in turn off land they did not possess. The poor rose up in revolt. So, the Gracchi brothers, first Tiberius then Gaius, sought to redistribute land to the poor from the acquisition of land from Pergamum. This redistribution angered the wealthy because Tiberius Gracchi went around the Senate.
Second, Roman leaders saw that they could gain more power if they helped the poor. So, people like Marius and Caesar (later on) sided with the cause of the people for political power. This, once again, angered the aristocracy.
Third, in time there were civil war fought among fellow Romans. Violence was at a high point. The proscriptions of Marius and Sulla were great and the civil wars were even more bloody.
Fourth, after a few generations of bloodshed, people cannot take it any more. Peace, no matter what the cost, is preferred, even if it means one strong leader. Augustus would be that leader and he would eventually start the Empire. In short, incessant civil wars created an Empire.