The Defeat of Amalek
While the Jews were still in Rephidim, the Amalekites, a mightily and fierce people, descendants of Esau, and well-trained in the art of warfare, suddenly attacked the people of Israel. It was an unprovoked and cowardly attack upon a tired and weary people, just liberated from slavery, on the way to their homeland.
Moses put his disciple Joshua in charge of the troops who were to fight against the Amalekites. Then Moses, together with his brother Aaron and nephew Hur, went up to a hill, to pray for G‑d's help in the battle. The battle lasted a whole day until the Amalekites were finally defeated and routed. G‑d ordered Moses to record the treacherous attack of the Amalekites for everlasting memory. Together with this memory went an oath to wipe the Amalekites — the incarnation of all evil — off the face of the earth. There could be no peace between Israel and Amalek for all time to come.
What about the Amalekites is the incarnation of all evil? What was different about them as opposed to all the other nations that came against Israel
Amalek in addition to attacking the Israelites unprovoked, did so with a few weeks of the great miracles of the 10 Plagues against Egypt as well as the splitting of the sea. When the Israelites left Egypt, no nation would attack them. Who would start up with a people whose G‑d just dealt the mighty Egypt a terrible defeat with ten awesome plagues, and drowned the surviving few in the sea? Only Amalek, driven by profound hatred which defied logic, came to wage battle. This means that despite G-d's miraculous mastery over Egypt, they still were untouched by that experience and decided to attack. This was a very powerful rebellion against G-d driven by the most powerful hatred for the Jewish People. Please see Wipe Out Amalek, Today? for a deeper insight about this.