Describe Rome's transition from a republic to an empire.

The Roman Republic was established around 509 B.C.E. The government they developed at the time and determined by existing conditions sought to establish laws that would limit power in the hands of a few. Thus, power was divided between the Senate (Roman Senate) and the general Roman citizenry (Plebeian Assembly). Divisions in the Republic were brought about by conflicts between the Senate and the Assembly.

The Senate was threatened by the growing strength of the Plebeian Assembly. This further degenerated into conflicts between the aristocracy and the common citizens. Roman expansion and existing conflicts led to a shift towards self-interest by various parties, causing a situation that the Republic sought to suppress. 

This led to the onset of civil wars, emboldened by the march on Rome by Sulla, who was later proclaimed dictator by the Senate. He, in turn, strengthened the Senate at the expense of the assemblies, permanently affecting the balance of power established earlier. More revolts followed, led by the likes of Marcus Lepidus, Pompey Magnus and Julius Caesar, all of whom marched on Rome to assert their authority.

Julius Caesar was later assassinated by members of the Senate. This led to the formation of the second triumvirate (Octavian, Antony and Lepidus) and marked the end of the Roman Republic. Fallout in the second triumvirate saw the rise of Octavian to absolute power. Under a new name referring to his new position, Caesar Augustus (Octavian) ushered a period of peace under Pax Romana that instituted remarkable growth of the Republic into the Roman Empire.

Describe the transition from the Roman Republic to an empire, ending with Julius Caesar.

It's actually somewhat difficult to discuss the early history of the Roman Republic, given how much of its history is mixed up with myth. As the Romans understood it, the Republic was preceded by rule of kings (beginning with Romulus, the founder of Rome, and ending with Tarquin). The last king was expelled and the Republic founded in its place.

Ultimately, the Republic evolved over the course of centuries. Roman history was largely shaped by the social conflict between the Patricians (Rome's dominant political and economic elite) and the far more numerous Plebians, with the Patricians having gradually been forced to grant concessions to the Plebians across the course of Roman history. The publishing of the Twelve Tables and the creation of the office of Tribune of the Plebs can be counted as critical moments in this history of social conflict and political evolution.

With the creation of Empire, these older political, economic, and social structures were transformed. Particularly important in this history, and in shaping the long term dissolution of the Republic, were the Marian Reforms, which involved a transformation of the Roman army, a service in which had been traditionally tied to property. Thus:

The army ... consisted of annual levies of amateur, peasant soldiers who were expected to supply their own weapons, food, and clothing, commanded by amateur officers who served a year and then returned to private life. ... Service in the army was seen as a duty and privilege of full citizens only, and those lacking the requisite amount of property, which constituted their "stock" in the corporate state, were excluded from this privilege (D. Brendan Nagle, The Ancient World: A Social and Cultural History, Prentice Hall: Upper Saddle River, New Jersey: 2002, p. 315)

However, to meet the demands of empire, Marius opened the military up to citizens without property. These reforms had the effect of tying the loyalty of Rome's soldiers more closely to their commanders, a fact which is powerfully illustrated in the history of the civil wars, and Caesar's own rise to power.

That being said, do note that while Julius Caesar plays an important role in this history, he did not himself mark the transition to Empire. After his defeat of Pompey, he did gain political supremacy in Rome, but he was killed in 44 BCE. Afterwards, there would be another round of civil wars, resulting in the rise of Octavius, who would become the first emperor, Augustus.

The Roman Republic began when the Romans, under Junius Brutus overthrew a particularly cruel Etruscan ruler, and the Roman Republic was proclaimed in 508 B.C.E. The Republic lasted for almost 500 years, with an unwritten constitution. It was probably the most stable form of government that the Roman people ever knew.

The Republic fought the Punic Wars with Carthage, and were successful; however it proved costly in the long run. Roman soldiers who fought in the war had been forced to abandon their farms to fight. As a result, when they returned from the war, their farms were in ruins and many lost everything to larger landowners. Since they had no means of supporting themselves, many Roman soldiers remained loyal to the generals under whom they had fought, including those who had fought with Julius Caesar.

The uncertainty of the times led to a bloody civil war, with one  Lucius Cornelius Sulla ultimately taking control. Sulla published a "proscribed list" of his enemies to be executed. Julius Caesar was one of those enemies, but Sulla did not consider him a threat; plus he was in Greece at the time and not a serious problem.

Julius Caesar spent large sums of his own money on circuses and gladiator fights which made him popular with the common people. He, along with Pompey and Marcus Crasus formed the first Triumvirate to rule the remains of the republic. Caesar was given command of Gaul, with the understanding that he would remain there. The Rubicon, a tiny river, was the line of demarcation which he was not to cross. Crasus died fighting in Mesopotamia; and when conservatives attempted to maneuver Caesar out of the government, he relied on his popularity to march on Rome. He is said to have uttered Jacta alia est when he crossed the Rubicon. (The phrase, "cross the Rubicon" is now used when one is said to have reached the point of no return.) When he arrived in Rome, Pompey fled to Egypt hoping to ally with Ptolemy IV and Cleopatra, but was murdered there. Caesar then moved into Rome and assumed the title of Dictator, an office provided for in the Roman Constitution in the event of a national emergency. Because members of the Senate feared Caesar would convert the Republic into a kingdom with himself as king, he was assassinated in 44 B.C.E.