I think Rome´s history is way too complex to put it in just one book, but Woolf did a good job. He tried to describe "what circumstances and technologies made the creation and maintenance of an empire possible, in just this place and just at that time" (on 378 pages).
The first chapter - called "The Whole Story" - gives a short summary of Rome`s rise and fall. The following chapters are like a collection of thoughtful essays on different topics like "who were the Romans?"; "how did Rome´s empire grow?"; "why did Rome succeed when its rivals failed"; "why did Rome`s expansion come to a stillstand or "why did the empire shrink until it was, once again, a city state". One chapter is dedicated to the emperors and their dynasties, another chapter portraits generals who influenced Rome´s fate like Sulla, Pompey and of course Julius Cesar. Woolf also tried to explain Rome`s decline which happened when the empire switched from polytheism to Christianity - coincidence?
Being an economist I enjoyed most when he describes the economic aspects of Rome´s rise & decline. In chapter 3 ("Rulers of Italy") the author outlines how a cluster of villages "gradually coalesced to form what by ancient standards was a massive city" and tried to explain "what factors made Rome emerge out of the general poverty of Latia culture to rival the great cities of Etruria" with the cities comparative advantage over its rivals. In chapter 4 "Imperial Ecology" (page 59) he speculates how climate changes might have influenced Rome`s rise and fall: The ascend was accompanied by a warmer climate which permitted better crops that could feed more people; the decline occurred in a chilling period. A colder climate might have inspired northern tribes to move south and to invade Rome. He also reports about advances in agriculture & transportation which made it possible to feed a million citizens.
The author also showed that the Greek had a strong influence on Rome´s culture - even as the city state had conquered their kingdoms & cities. Even imprisoned and enslaved Greek were highly respected in Rome´s society.
Woolf also described the importance of slavery for Rome`s economy: "Slaves worked in the fields and the mines, served at the table and in he bedroom, were teachers" They were luxury "the price in today`s terms is about that of a new car". But "Romans famously freed many of their slaves and gave them a limited form of citizenship.
"Rome - An Empire´s Story" is a valuable introduction into Rome´s complex and rich history, especially that Woolf adds a lot of additional sources and refers to plenty of further reading.