Because it is surrounded by deserts like the Land of Oz, Egypt is pretty hard to invade. So a lot of the time Egypt was at peace. But not all the time. The Egyptians fought among themselves over who would be in charge of their country, and over whether the country would be united (as in the First Intermediate Period).
The Egyptians also sometimes fought off invasions from the Libyans to their west, or from the Nubians to their south (and sometimes they lost to these attacks too). Around 1700 BC, there was a big invasion of Hyksos from the north.
Beginning as early as the Middle Kingdom, Egyptian pharaohs hired Nubian mercenaries from Sudan to fight in their wars. It is likely (though not proven) that the New Kingdom Egyptians hired Greek mercenary soldiers to fight in their wars with them about 1500 BC. Certainly many Greek soldiers fought for Egypt while Egypt was revolting against Persian rule in the 500s and 400s BC.
Eyewitness: Ancient Egypt, by George Hart. Easy reading.
The Oxford History of Ancient Egypt, by Ian Shaw (2002).
History of Ancient Egypt: An Introduction, by Erik Hornung (1999). A college textbook. On the conservative side – not much on new developments.
Ancient Near Eastern History and Culture, by William H. Stiebing (2002). Expensive for a paperback, but brief and very up to date. And yes, it includes Egypt in the Near East.