Caligula's real name was Gaius Julius Caesar Augustus Germanicus (after his ancestors Julius Caesar and Augustus), but everyone called him Caligula because when he was a little boy he lived in military camps where his father was the general, and he wore little soldier boots, so the soldiers called him "Little Boots", which is Caligula in Latin.
A Roman soldier's sandal, or "caliga"
Caligula's father, Germanicus, was Augustus' adopted grandson, and Caligula's mother, Agrippina the Elder, was Augustus' granddaughter. Caligula was born on August 31st, 12 AD. He had four brothers and three sisters. Two of Caligula's brothers died before they grew up. Caligula's father also died when Caligula was only seven. It's possible that the emperor Tiberius poisoned Caligula's father to get him out of the way. After his father died, Caligula's mother Agrippina got into a long fight with Tiberius about whether he had really poisoned him.
More about Caligula
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.
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.