Saul did not listen. If you read further into I Samuel, you will find out what happened to him.

As for Amalek Exodus 17:8 and Numbers 14:45 will tell you thier history of attacking Israel.

Here's a description of the history from biblegateway/Encyclopedia of The Bible:

AMALEK ăm’ ə lĕk, AMALEKITES ăm’ əl’ ĕk īts (עֲמָלֵ֑ק, עֲמָלֵקִ֗י; Gr ̓Αμαλήκ, ̓Αμαληκίτης). An ancient marauding people in the S of Canaan and the Negeb who were fierce enemies of Israel particularly in the earlier part of her history.

1. Early history. Amalek was one of the sons of Eliphaz and a grandson of Esau (Gen 36:15, 16; 1 Chron 1:36). He was born to Eliphaz by his concubine Timna (Gen 36:12) was one of the tribal chiefs (אַלּוּפ֮, H477) of Edom (Gen 36:16, 17). There is an earlier reference to the word Amalek in Genesis 14:7 where Chedorlaomer (c. 1900 b.c.) and his associate kings subdued among others, “all the country of the Amalekites,” which reference need not be taken as an anachronism, but is to be understood as possibly a different Amalek, or better, that the term is used to identify the land which later became the home of the Amalekite descendants of Esau. In Numbers 24:20 Balaam prophesied, “Amalek was the first of the nations, but in the end he shall come to destruction.” This reference does not suggest that the early Genesis 14:7 reference to Amalek is in conflict with the Genesis 36:16 statement regarding Amalek, the grandson of Esau. Rather in Numbers 24:20 Amalek as first is to be understood as its being the first among the nations to attack Israel in her Exodus experiences (cf. Exod 17:8; Num 14:45).

2. Territory. The Amalekites as a nomadic desert tribe moved in the area from the Sinaitic region and the steppe land of the Negeb in S Canaan, S of Beersheba, over E to include the Arabah region N of Elath and Ezion-geber and possibly the more interior Arabia. See 1 Samuel 15:7 where Saul is said to have “defeated the Amalekites, from Havilah as far as Shur, which is east of Egypt.” This seems to have been the same general area inhabited by the Ishmaelites about whom it is stated: “They dwelt from Havilah to Shur, which is opposite Egypt in the direction of Assyria” (Gen 25:18). 1 Samuel 30:1, 2 points to the Amalekite heavy raiding activity in the area of the Negeb, and Judges 6:3, 33 in speaking of the Amalekite association with the kings of the E in their raiding parties suggests that they may have lived sometime together in the Arabian territory toward the E.

The Amalekites also extended their influence farther N into the Philistine country and the region of Ephraim. This is borne out by Judges 12:15 where the area of Ephraim around the town Pirathon (not far from present-day Nablus) is called “the hill country of the Amalekites.” See 1 Samuel 27:5-7 and 30:1 for the fact that Amalek raided Philistine towns like Ziklag (a few m. N of Beersheba) which Achish, king of Gath, had given to David.

3. Amalek and Israel.

a. In the wilderness wanderings. Exodus 17 describes Israel’s first encounter with the wandering Amalekites at Rephidim, a place between the wilderness of Sin and the wilderness of Sinai (Exod 17:1; 19:2), at which the Israelites camped in their Exodus journey from Egypt. At this place, following the Amalekite attack, Israel defeated her enemy (Exod 17:8-16). Concerning further harassment Moses recounts how, in Israel’s journey from Egypt, Amalek, with no fear of God, attacked their rear guard and cut off those who became physically weak (Deut 25:17, 18). Moses goes on to command that for this wicked treatment of an oppressed people, Israel later, when in the land of Canaan, was to exterminate the Amalekites (Deut 25:19). That Amalek’s unrelenting and destructive spirit and action against God and the cause of His people Israel was heinous to the Lord is seen later in the reminder to Saul concerning these wilderness incidents and in God’s command that the king is to destroy these God-defying Amalekites (1 Sam 15:2, 3; cf. also Judg 10:12). Thus, the continuing oppressive spirit of this pagan nomadic tribe required a different treatment by the Lord from that which was to be normally carried out; namely, that terms of peace be first offered to a potential enemy (Deut 20:10-12).

After Rephidim, the next major encounter with Amalek came following the report of the spies to Israel that the enemy to the N of Kadesh-barnea in the wilderness of Paran in S Canaan, including the Amalekite forces which dwelt “in the land of the Negeb,” were too strong to conquer, despite the pleadings of Caleb and Joshua to the contrary (Num 13:25-33; 14:38). Israel rebelled. When God in judgment withdrew His hand of blessing and ordered them to go back S into the wilderness (14:1-25), the people again disobeyed God, and with their own feeble effort attacked the Amalekites. They were completely defeated and chased as far as Hormah (near Arad and Ziklag) (Num 14:39-45; Josh 12:14; 15:30). The reason for the Lord’s concern about disobedient Israel’s encountering Amalek and other enemies without His special power was that the Amalekites who dwelt in both the hill country and in the valleys of S Canaan and the Negeb, were effective fighters in both areas (Num 14:25, 44, 45).

b. In the period of the Judges. Later in the time of the Judges the Amalekites showed continued harassing activity against Israel. When some men of Judah went down to fight against the Canaanites who exercised some control over the Negeb and the area of Hebron, presumably they also came in contact with the Amalekites who roamed the same general area. This is seen by observing the Kenites who lived with the Amalekites at the city of Amalek (1 Sam 15:5, 6) and that they earlier had taken up this residence with the people in the region of the Negeb near Arad (Judg 1:16), which was only about twenty m. S of Hebron. Observing this connection, there is no need, as some have attempted, to emend the text of Judges 1:16 from “the people” (Heb. הָעָֽם; LXX ὁ λαός) to Amalekite (עֲמָלֵקִ֗י), to try to make agreement with 1 Samuel 15:6, since the connection of the Kenites in these two passages is clear and evidence for changing the text is lacking.

Within this period of the Judges the Amalekites were associated with the Moabites, Ammonites, and Midianites in their marauding activities. This is seen in Judges 3:12-14 in the account of how Eglon, the king of Moab, collected the forces of the Amalekites and the Ammonites and defeated Israel and took the city of palms (evidently Jericho, cf. Deut 34:3). Further, in their song (Judg 5:14) Deborah (who was from Ephraim, 4:5) and Barak speak of how Ephraim had shown strength in rooting out those of the Amalekites who were in its midst (cf. Judg 12:15 and remarks earlier). The RSV in Judges 5:14 wrongly changes the words “in Amalek” to “into the valley,” although that v. indicates in a footnote that the Heb. and Gr. read “in Amalek.” Judges 6:3, 33; 7:12 depict the Amalekites joining forces with the Midianites (who seem to have wandered in the area of Sinai [Exod 4:19] and wilderness E of Paran [1 Kings 11:18]; and also in the territory E of Gilead [Judg 8:4-12]), and making camel raids against the agriculture communities of Israel as far S as Gaza (6:3, 4). When these peoples came with considerable forces and camped in the Valley of Jezreel (6:33), Gideon and his 300 men, under the direction of the Lord, routed and killed many of them (7:19-23).

c. In the time of Saul. 1 Samuel 14 and 15 present Saul’s encounter with the Amalekites. According to 1 Samuel 14:47, 48 the king had fought against this enemy. However, in 1 Samuel 15:2 this people were still flourishing. In the light of Amalek’s past harassment of Israel the Lord commanded Saul to exterminate this enemy (1 Sam 15:1-3). The king attacked and conquered this foe with their city called Amalek (1 Sam 15:4-7) the exact location of which is not known. Evidently the Amalekites had some cities, as this one, in which they sometimes settled, and possibly fulfilled religious obligations as has been shown was the case of nomadic tribes in the Trans-Jordan in connection with a 15th cent. b.c. temple (E. F. Campbell and G. E. Wright, “Tribal League Shrines in Amman and Shechem,” BA, XXXII, No. 4 [Dec., 1969], 104-111). Contrary to God’s command, Saul kept alive the Amalekite king and the best of their livestock (vv. 8, 9). For Saul’s failure to fulfill completely the divine command, Samuel announced to the monarch the Lord’s rejection of him as king (1 Sam 15:10-23). Saul then made a statement of repentance and obtained some public reconciliation with the prophet Samuel, following which the prophet then killed Agag, the Amalekite king (15:24-33).

d. In the time of David. David’s initial encounter with the Amalekites, in the OT record, took place during the time of his association with Achish, king of Gath, when the young Israelite made raids in the S against the Amalekites and others (1 Sam 27:8). Later Amalek raided the Negeb and, in David’s absence, completely conquered Ziklag, taking captive the inhabitants including David’s two wives, Ahinoam and Abigail (1 Sam 30:1-6). Then the future king, through the help of an abandoned Egyp. servant of an Amalekite (30:11-15), found the Amalekite camp, defeated the enemy, and recovered his wives and possessions (30:16-20).

Next, the Amalekite who claimed he had finished killing Saul (cf. 1 Sam 31:3-5; 2 Sam 1:4-10) was killed by David because he had slain “the Lord’s anointed” king (1:14-16), and also had confessed he was an Amalekite (1:8, 13). This demonstrates again Israel’s strong antipathy to Amalek. The psalmist (Ps 83:7) lists Amalek with the avowed enemies of Israel. A summary of David’s conquests of Amalek is given in 2 Samuel 8:12 and 1 Chronicles 18:11.

4. Amalek in later history. The Amalekites seem to have been fairly well controlled under the monarchy, for the OT does not mention them again until the time of Hezekiah (c. 700 b.c.) and only as a remnant whom some of the Simeonites defeated at Mount Seir (i.e., Edom; Gen 32:3; 1 Chron 4:41-43). There is no further Biblical reference.

Bibliography G. A. Smith, The Historical Geography of the Holy Land (1896), 282; D. Baly, The Geography of the Bible (1957), 159.