Amalek
Amalek is the most abominable of all nations. They were the first to wage war against Yisroel ("who happened upon you on the way when you were leaving Mitzrayim, and you were tired and weary, and (Amalek) did not fear Elokim"). They went to war against Yisroel before their entry into Eretz Yisroel, and they will be the last to fight against Yisroel before the coming of Moshiach.
Chazal explain that when Bnei Yisroel left Mitzrayim, all nations feared them as mentioned in the possuk "The nations heard and trembled," etc. When Amalek came and fought with Yisroel, they caused the fear of Hashem's protection over Bnei Yisroel to diminish.
This is comparable to a parable of a boiling bath that everyone is afraid to enter until one person enters and gets burned - although they got burned, they still cooled the bath for everyone else.
Hashem's War Against Amalek
The Torah states two things about this war:
- Hashem commands Moshe "You shall utterly erase the memory of Amalek." This mitzvah is one of the mitzvos dependent on Bnei Yisroel's entry into Eretz Yisroel, as the Rambam states: "Three mitzvos were commanded to Yisroel upon entering the land - to appoint a king, to destroy the seed of Amalek, and to build the Beis Hamikdash."
- "Hashem swore that His name and throne would not be complete until the seed of Amalek is destroyed" ("For the hand is on the throne of Hashem, Hashem will have war with Amalek from generation to generation"), and in the Geulah when Melech HaMoshiach will erase the seed of Amalek, it is said: "On that day, Hashem will be One and His Name will be One."
When Shaul was appointed king over Yisroel, Hashem commanded him through Shmuel HaNavi to fight Amalek and not leave even one of them alive, even commanding to kill all their animals.
Shaul fought Amalek but did not fully fulfill Hashem's command and left Agag, king of Amalek, and the choice sheep alive (wanting to elevate them to kedushah). When Shmuel came and saw this, he beheaded Agag.
For this incident, Shaul was punished by having his kingship taken from him and given to Dovid, who possessed kabolas ol - "Dovid My servant."
That night that Agag remained alive, he brought a son into the world who continued Amalek's existence in the world, and from him was later born Haman who wanted to destroy all the Yidden.
When Sancheriv came and mixed up the nations (so they would feel his dominion over them), many nations lost their identity, and Amalek also lost its identity. Therefore, Amalek exists even now but we don't know who they are, and when we are redeemed in the true and complete Geulah, the seed of Amalek will be recognized and cut off.
Amalek in Chassidus
According to Chassidus, Amalek is an eternal spiritual reality, like all Torah stories and commandments which are eternal and provide instruction for every Yid in every place and time.
Amalek represents the essence of evil within every Yid, which interferes with and opposes everything holy without any reason. Its nature is 'coldness' - cooling every Godly matter so one shouldn't be moved by anything, and if one is moved, Amalek works to prevent that inspiration from causing any real and essential change in the person. It is the root of all bad middos.
While other bad middos can be driven from one's heart through the avodah of davening, where a person internalizes Hashem's unity and thereby reaches ahavas Hashem, Amalek cannot be "convinced" of Hashem's goodness since its nature is chutzpah and arrogance without reason (this is why Chassidim had such great hatred for Amalek).
While the kelipah in other nations comes from the concealment of Godly life-force, Amalek is different in that the aspect of daas is not hidden from them - they know their Master and intend to rebel against Him out of chutzpah and boldness without any reason.
Therefore, the way to wage spiritual war against Amalek is also through elevation and transcendence above reason and daas, an elevation that comes from the essential good and holiness within each person (etzem haneshama). The essence of this war is 'tekias hadaas' and connection to Elokus with the strength that comes from etzem haneshama.
See Also
Shabbos Zachor