New Kingdom Egypt
With the reunification of Egypt by the southerner Ahmose (Kamose died before it was united) and the expulsion of the Hyksos, Egypt began a new period of prosperity under the 18th dynasty. At this time there was a great deal of trade with Western Asia, and Egyptian armies even conquered much of Israel and Syria, though they were constantly fighting the Hittites and Assyrians to keep control of it. Great temples were built all over Egypt. The Egyptian queens were very powerful at this time, and in 1490 BC one of them, Hatshepsut, became Pharaoh herself. Hatshepsut's reign was long and peaceful, and she built up many trading agreements with African kingdoms south of Egypt that made Egypt much richer than before.
In 1303 BC a new northern dynasty or family of Pharaohs took over, the 19th Egyptian dynasty. Their first king, Rameses, moved the capital back to Memphis in the north. Priests became very powerful. Fighting with the Hittites in West Asia continued, but also a lot of trade. This is the time when the Bible says the Jews were slaves in Egypt.
The 20th dynasty Pharaohs, around 1200 BC, continued the same policies, and were all called Rameses. There were many attacks on Egypt, first from Libya to the west and then from West Asia, by a group that the Egyptians called the Sea Peoples. The Hittites were destroyed, though around 1100 BC the Egyptians fought off the Sea Peoples in a great naval battle. But the trouble in West Asia seems to have caused a general economic depression in the whole Eastern Mediterranean and West Asia, and soon afterwards the New Kingdom collapsed.
To find out more about New Kingdom Egypt, check out these books from Amazon or from your library:
Eyewitness: Ancient Egypt, by George Hart. For kids.
The Oxford History of Ancient Egypt, by Ian Shaw (2002).
Rulers of Ancient Egypt, by Russell Roberts (1999). Includes chapters on Hatshepsut, Akhenaten, Tutankhamon, Rameses II, and (oddly) Cleopatra, who ruled much later. For kids.
Chronicle of a Pharaoh: The Intimate Life of Amenhotep III, by Joann Fletcher (2000). Amenhotep III was the father of Akhenaten. For high schoolers.