The Roman Republic
Now the Romans began to conquer southern Italy. They used another good idea to help them. Like Alexander the Great about the same time, Romans told everybody that if any city needed help fighting a war, the Romans would be happy to help them. Soon a city did ask for help, when its neighbors were attacking it. The Romans sent soldiers and fought off the neighbors. But when the war was over, the Romans announced that they were going to leave Roman soldiers in this city, to keep the city safe. But when there are Roman soldiers living in the middle of your city, you pretty much have to do whatever the Roman Senate says! On the other hand, the Romans also copied the Persians and Alexander by including the conquered cities as Romans, so they would come to feel that they were Romans themselves. In this way the Romans took over all of southern Italy.
Toward the end, some of the Greek cities in southern Italy asked for help from Pyrrhus (PIRR-us), the king of Epirus (eh-PEER-us), who was also Greek. Pyrrhus thought he would be like Alexander the Great and conquer the world, so he came with many men and elephants (the elephants came from India). But the Romans beat Pyrrhus too.
Classical Rome, by John Clare (1993). For kids, the whole political history from beginning to end.
Oxford First Ancient History, by Roy Burrell (reissued 1997). Easy reading. It skips around a lot, not trying to tell everything, just highlights.
The Romans: From Village to Empire, by Mary Boatwright, Daniel Gargola, and Richard Talbert (2004). Okay, it's a little dry, but it is up to date and has all the facts you could want.
The Beginnings of Rome: Italy and Rome from the Bronze Age to the Punic Wars (c. 1000-264 BC), by Tim Cornell (1995). A little more specialized.