The Roman Empire was the post-Republican period of the ancient Roman civilization, characterised by an autocratic form of government and large territorial holdings in Europe and around the Mediterranean. The term is used to describe the Roman state during and after the time of the first emperor, Augustus.
The 500-year-old Roman Republic, which preceded it, had been weakened and subverted through several civil wars.[nb 2] Several events are commonly proposed to mark the transition from Republic to Empire, including Julius Caesar's appointment as perpetual dictator (44 BC), the Battle of Actium (2 September 31 BC), and the Roman Senate's granting to Octavian the honorific Augustus (4 January 27 BC).[nb 3] Roman expansion began in the days of the Republic, but the empire reached its greatest extent under Emperor Trajan: during his reign the Roman Empire controlled approximately 6.5 million km2 of land surface. Because of the Empire's vast extent and long endurance, the institutions and culture of Rome had a profound and lasting influence on the development of language, religion, architecture, philosophy, law, and forms of government in the territory it governed, particularly Europe, and by means of European expansionism throughout the modern world.
In the late 3rd century AD, Diocletian established the practice of dividing authority between four co-emperors, in order to better secure the vast territory, putting an end to the Crisis of the Third Century. During the following decades the empire was often divided along an East/West axis. After the death of Theodosius I in 395 it was divided for the last time.
The Western Roman Empire collapsed in 476 as Romulus Augustus was forced to abdicate by Odoacer. The Eastern Roman or Byzantine Empire ended in 1453 with the death of Constantine XI and the capture of Constantinople by the Ottoman Turks led by Mehmed II.
The above extract is taken from the following link http://en.wikipedia.org/wiki/Roman_Empire
Below are photographs of four wall panels in central Rome which depict the spread of the Roman Empire. (My apologies for the poor quality of the images).
Figure 1: Initially, the Roman Empire was in Rome (where it is marked with a white circle on the map).
Figure 2: Then the Roman Empire began to grow and spread (see the areas marked in white).
Figure 3: The Roman Empire continued to grow and expand ...
Figure 4: At its height, the Roman Empire covered a large proportion of Europe, the whole of Turkey, North Africa and parts of the Middle East.
The following website provides a better map which gives a clearer indication of the extent of the modern day countries which the Roman Empire occupied http://www.roman-empire.net/maps/empire/extent/rome-modern-day-nations.html