Five Good Emperors
When Domitian was assassinated in 96 AD, people were very much afraid that it would be like after the assassination of Julius Caesar, or after Nero's suicide, and there would be another civil war. Quickly the Senate met and chose one of the senators to be emperor.
They chose Nerva, who was an old man with no sons who might want to inherit the throne. Nerva didn't have time to do much as emperor, because he died in 98 AD, after only two years in power, but he did start a new system for choosing the next emperor which worked better: he chose somebody who seemed like he would do a good job, and he adopted him as his son.
The man Nerva adopted was Trajan. And Trajan did become emperor when Nerva died, and he did do a good job. Trajan took the Roman army to Dacia (modern Rumania), and he conquered it. Dacia had a lot of gold mines, and so Rome became rich from all the gold. Trajan also seems to have made Christianity illegal. Then Trajan took the army to West Asia, and he conquered a lot of land from the Parthians - all the way to Babylon, where Alexander had died! Trajan also had no sons, and he seems to have adopted his nephew as HIS son. The nephew's name was Hadrian.
When Trajan died, Hadrian became emperor. Hadrian was not as popular as Trajan, because as soon as Trajan died Hadrian decided that the Roman Empire couldn't really keep all that land Trajan had conquered in West Asia, and he gave most of it back to the Parthians. He thought it would be too expensive to try to keep it, because it was so far away from Rome. Of course the army didn't like giving up all this land they had fought for. And Hadrian didn't try to conquer anyplace new either. The army got bored. Still, Hadrian did keep peace in the Roman Empire. Like Nerva and Trajan, Hadrian had no children, and he adopted a grown man instead.
This is Hadrian's wife, Sabina.
When Hadrian died in 134 AD, his adopted son Antoninus became emperor. Antoninus is often called Antoninus Pius because he was so interested in religion and in doing everything right. Like Hadrian, he didn't fight any wars. But the Roman Empire stayed peaceful and everyone was doing pretty well. Again Antoninus Pius adopted a grown man to follow him, and that was Marcus Aurelius.
This is Antoninus Pius' wife, Fausta, and his family
Classical Rome, by John Clare (1993). For kids, the whole political history from beginning to end.
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 Roman Empire, by Colin Wells (1984). More readable. Alternates chapters on political and social history. Unfortunately, he stops at the third century crisis.
The Roman Succession Crisis of AD 96-99 and the Reign of Nerva, by John Grainger (2002).
Trajan: Optimus Princeps, by Julian Bennett (2001).
Memoirs of Hadrian, by Marguerite Yourcenar (1963). A famous historical novel, written through the eyes of Hadrian.