Claudius was born in 10 BC in the city of Lugdunum in Gaul (modern Lyons, France). His mother was Antonia Minor, Mark Anthony‘s youngest daughter with Octavia, and his father was Drusus, Tiberius‘ younger brother.
Because his mother was the emperor Augustus‘ niece, Claudius was related to Augustus. And his uncle Tiberius was in line to become emperor, so Claudius was an important person even as a child. He had an older sister and an older brother, Germanicus (who grew up to be Caligula‘s father).
Claudius’ father died suddenly when Claudius was only a year old, and he was raised by his mother Antonia and his father’s mother Livia. They hired the historian Livy (who was from Livia’s clan) to teach him history.
Claudius had physical challenges, and his mother thought he would not be able to be a politician. He stammered, and his head shook, and his knees were weak, and he salivated too much when he was excited. He may have been sick with a rare illness called Wilson’s Disease, that can also make people psychotic (crazy). Caligula may have had the same disease. Or it might have been cerebral palsy.
Because he was sick, Claudius stayed home most of the time and did not go to parties or join the army, and he didn’t run for election to anything. Mostly he read books, and wrote histories and scientific papers. So Augustus, Tiberius, and Caligula didn’t notice him, and they didn’t think to kill him when they were killing most of their other relatives.
But in 37 AD, when Claudius was 46 years old, Caligula did decide to make his uncle Claudius consul. Probably he wanted to remind people how much they had liked Caligula’s father (Claudius’ brother) Germanicus. Caligula made fun of Claudius and bullied him all the time, and made Claudius miserable. But people noticed Claudius more because of that.
Then four years later when Caligula was killed, people realized that Claudius was the only living man descended from Augustus, so they made him emperor. Claudius was now 50 years old. People must not have been expecting much, but actually Claudius turned out to be a good emperor – his disabilities didn’t keep him from being a smart guy.
Claudius made the Roman Empire even bigger than it already was by sending armies to conquer Britain (modern England), and by political takeovers of other places, including Judaea (modern Israel). He also worked to make the court system fairer, although he was easy to persuade and sometimes not as fair as he wanted to be. He also gave slaves more rights than they had had before. And he built a great port at Ostia, to make it easier to bring wheat into Rome from Africa and Egypt by ship.
Even so, many Senators hated Claudius and tried to kill him. Because of this, he didn’t trust Senators, and he used mainly freed slaves as his helpers. Of course this made the Senators hate Claudius even more. But in the end Claudius was poisoned by his wife Agrippina the Younger, who wanted power for herself and her son Nero. Claudius died in 54 AD, when he was 64 years old, probably from eating poisonous mushrooms.
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 Roman Revolution, by Ronald Syme (1960). Still a classic.
From the Gracchi to Nero: A History of Rome from 133 B.C. to A.D. 68
by H. H. Scullard (1959, 5th edition 1990). Another classic.