The first people to live along the North African coast were Berbers, nomadic shepherds and cattle herders who spoke a Hamitic language related to Ancient Egyptian and probably were a genetic mixture of people from West Asia with people from southern Africa. These people frequently invaded Egypt, where they were called the Libyans, and sometimes they had a lot of power in Egyptian politics. But about 800 BC, Phoenician colonists arrived from West Asia and started the city of Carthage, in modern Tunisia. Carthage had a good port, and an important military location. It is located at a narrow point of the Mediterranean Sea, opposite the island of Sicily, and a navy that controls both southern Sicily and Carthage (as the Phoenicians did) can control shipping in the Mediterranean. Because of this, Carthage quickly grew into an important city.
When the Persians conquered Phoenicia in the late 500s BC, Carthage gained its independence. The Persians had no navy, and were not that interested in the Mediterranean, so Carthage was able to become an independent country. In addition to North Africa and southern Sicily, Carthage also controlled a lot of Spain, including some important silver mines there.
El Madayan: An Islamic City Through the Ages
by Abderrahman Ayoub, Jamila Binous, Abderrazak Gragueb (1994)
Hannibal (First Book) by Robert Green (1997)
The Young Carthaginian by G. A. Henty (1860s, reprinted 2001) This is a good adventure story that can introduce kids to the wars between Rome and Carthage, but because it was written more than 100 years ago, it has some racist and unfair assumptions about the Romans being better people than the Carthaginians - watch out!
The Late Roman West and the Vandals by Frank M. Clover (not a kids' book) (1993)