When Julius Caesar visited Egypt, the Ptolemaic (Greek) Pharaoh of Egypt, Cleopatra, begged him to help her fight a civil war against her teenaged brother and husband, Ptolemy.
Julius Caesar did help Cleopatra get back into power, but he left Roman troops all over Egypt, and also took Cleopatra (klee-oh-PAT-rah) back to Rome with him as his girlfriend, where they had a baby. When Julius Caesar was assassinated in Rome in 44 BC, Cleopatra went back home to Egypt with another Roman leader, Mark Anthony (who was also her partner). Cleopatra ruled Egypt for another fourteen years, raising three more children with Mark Anthony and running her country successfully while also managing Roman politics so Egypt could stay independent.
In a civil war between Julius Caesar's nephew Augustus and Marc Anthony, however, Antony and Cleopatra were finally defeated. They killed themselves (or perhaps were killed) in 30 BC, and the Romans took over Egypt.
The Romans valued Egypt very highly, because it was so fertile and produced so much food. A lot of food, especially wheat for bread, was taken from Egypt for taxes and sent to Rome on big ships. To make it easier to collect these taxes, the Romans also established Roman-style government in Egypt, though the main language of government was still Greek (the way it had been under Greek rule) rather than Latin. By this time even most ordinary people in Egypt knew some Greek. Gradually people stopped writing hieroglyphs and wrote mostly in the Greek alphabet.
Learn by doing: read Shakespeare's Julius Caesar and Anthony and Cleopatra
Go on to Islamic Egypt
Asterix and Cleopatra, by Rene Goscinny. A funny comic book, but historically not so far off.
Cleopatra, by Diane Stanley (reprinted 1997) . A biography of the last independent queen of Egypt, for kids.
Egypt After the Pharaohs: 332 BC-AD 642: from Alexander to the Arab Conquest, by Alan Bowman (1996). A standard among historians, and pretty readable.
Women in Hellenistic Egypt: From Alexander to Cleopatra, by Sarah Pomeroy (reprinted 1990). Pomeroy is an expert on the lives of women in antiquity.
The Hellenistic World and the Coming of Rome, by Erich Gruen (reprinted 1986).
Life in Egypt Under Roman Rule, by Naphtali Lewis (1999). A classic work, which uses evidence from scraps of writing on papyrus - shopping lists, letters, contracts, bills - to reconstruct people's daily life.
Egypt in Late Antiquity, by Roger S. Bagnall (reprinted 1995).
Old Kingdom (2686-2160
First Intermediate Period (2160-2040 BC)
Middle Kingdom (2040-1633 BC)
Second Intermediate Period (1786-1558
New Kingdom (1558-1085 BC)
Third Intermediate Period (1085-525 BC)
Persian rule (525-332 BC)
Greek rule (332-30 BC) (also called the Hellenistic)
Roman rule (30 BC-700 AD)
Islamic rule (700 AD to 1500)
Dress up as Cleopatra!
A Cleopatra costume for Halloween or for acting out Cleopatra's story
A Cleopatra costume for younger people, in a smaller size
Julius Caesar costume (also works for Mark Anthony)