Abraham in Judaism

Abraham is considered the father of the Jewish nation, as their first Patriarch, and having a son (Isaac), who in turn gave birth to Jacob, and from there the Twelve Tribes. To father the nation, God "tested" Abraham with ten tests, the greatest of which being the sacrifice of his son Isaac. God promised the land of Israel to his children, and that is the first claim of the Jews to Israel.
Judaism ascribes a special trait to each Patriarch. Abraham's was kindness. Because of this, Judaism considers kindness to be an inherent Jewish trait.
Jewish tradition teaches the origins of Abraham's monotheism. His father Terah owned a store that sold idols. Abraham (then Abram), at the age of three, started to question their authenticity. This culminating in Abraham destroying some idols.
Abraham was then brought to the king, and sentenced to death, along with his brother Haran, unless they recanted their position. Abraham did not, and was thrown into a fire. When Abraham exited unscathed, Haran also would not recant, and was thrown into the fire. Haran, who did not truly believe, died in the fire. This is hinted to in Genesis 11:28.
Abraham then went to Haran (the city, different name than his brother) with his father and brother. His father died there. God spoke to Abraham for the first time, and told him of great things He would give him if he would leave Haran. Abraham did. He was seventy-five during this affair.
Abraham started a school for teaching his beliefs in God, and some say he wrote the Sefer Yetzirah.
Jews today mention Abraham in their prayers, when praying to "the God of Abraham". And, because of Genesis 15:1, ask that God shield them, like he promised to shield Abraham. Also, the epitome of his tests, the binding of Isaac on the altar, is mentioned many times in the Jewish liturgy.

Abraham in Genesis

The account of his life is found in the Book of Genesis, beginning in Chapter 11, at the close of a genealogy of the sons of Shem (which includes among its members Eber, the eponym of the Hebrews).
His father Terah came from Ur of the Chaldees, identified by most historians with the ancient city in southern Mesopotamia which was under the rule of the Chaldeans — although some believe that "Ur" should be identified with Urfa (or Ur-Of-The-Khaldis) in northern Mesopotamia, in keeping with the local tradition that Abraham was born in Urfa; or with the nearby Urkesh, which others identify with "Ur of the Chaldees". They also say "Chaldees" refers to a group of gods called Khaldis while the Urartian language is also known as Chaldaean thanks to Josephus. Abram migrated to Haran, apparently the classical Carrhae, on a branch of the Habor. Thence, after a short stay, he, his wife Sarai, Lot (the son of Abram's brother Haran), and all their followers, departed for Canaan. There are two possible Ur cities not far from Haran; Ura and Urfa, a northern Ur also being mentioned in tablets at Ugarit, Nuzi, and Ebla. These possibly refer to Ur, URA, and Urau (See BAR January 2000, page 16). Moreover, the names of Abram's forefathers Peleg, Serug, Nahor and Terah, all appear as names of cities in the region of Haran (Harper's Bible Dictionary, page 373). Yahweh called Abram to go to "the land I will show you", and promised to bless him and make him (though hitherto childless) a great nation. Trusting this promise, Abram journeyed down to Shechem, and at the sacred tree (compare Gen. 25:4, Joshua 24:26, Judges 9:6) received a new promise that the land would be given unto his seed (descendants). Having built an altar to commemorate the theophany, he removed to a spot between Bethel and Ai, where he built another altar and called upon (i.e. invoked) the name of Yahweh (Gen. 12:1-9).
Here he dwelt for some time, until strife arose between his herdsmen and those of Lot. Abram thereupon proposed to Lot that they should separate, and allowed his nephew the first choice. Lot preferred the fertile land lying east of the Jordan River, whilst Abram, after receiving another promise from Yahweh, moved down to the oaks of Mamre in Hebron and built an altar.
In the subsequent history of Lot and the destruction of Sodom and Gomorrah, Abram appears prominently in a passage where he intercedes with Yahweh on behalf of Sodom, and is promised that if ten righteous men can be found therein the city shall be preserved (18:16-33).
Driven by a famine to take refuge in Egypt (26:11, 41:57, 42:1), Abram feared lest his wife's beauty should arouse the evil designs of the Egyptians and thus endanger his own safety, and alleged that Sarai was his sister. This did not save her from the Pharaoh, who took her into the royal harem and enriched Abram with herds and servants. But when Yahweh "plagued Pharaoh and his house with great plagues" suspicion was aroused, and the Pharaoh rebuked the patriarch for his deceit and sent him away under an escort (12:10-13:1).
There is a parallel text describing a similar event at Gerar with the Philistine king Abimelech.
As Sarai was infertile, God's promise that Abraham's seed would inherit the land seemed incapable of fulfilment. His sole heir was his servant, who was over his household, a certain Eliezer of Damascus (15:2). Abraham is now promised as heir one of his own flesh. The passage recording the ratification of the promise is remarkably solemn (see Genesis 15).
Sarai, in accordance with custom, gave to Abram her Egyptian handmaid Hagar, who, when she found she was with child, presumed upon her position to the extent that Sarai, unable to endure the reproach of barrenness (cf. the story of Hannah, 1 Samuel 1:6), dealt harshly with her and forced her to flee (16:1-14). Hagar is promised that her descendants will be too numerous to count, and she returns. Her son Ishmael thus was Abram's firstborn (and Islamic doctrine holds that he was the rightful heir). Hagar and Ishmael were eventually driven permanently away from Abram by Sarah (chapter 21).
The name Abraham was given to Abram (and the name Sarah to Sarai) at the same time as the covenant of circumcision (chapter 17), which is practiced in Judaism to this day. At this time Abraham was promised not only many descendants, but descendants through Sarah specifically, as well as the land where he was living, which was to belong to his descendants. The covenant was to be fulfilled through Isaac, though God promised that Ishmael would become a great nation as well. The covenant of circumcision (unlike the earlier promise) was two-sided and conditional: if Abraham and his descendants fulfilled their part of the covenant, Yahweh would be their God and give them the land.
The promise of a son to Sarah made Abraham "laugh," which became the name of the son of promise, Isaac. Sarah herself "laughs" at the idea, when Yahweh appears to Abraham at Mamre (18:1-15) and, when the child is born, cries "God hath made me laugh; every one that heareth will laugh at me" (21:6).
In Genesis 18, Abraham pleads with God not to destroy Sodom, and God agrees that he would not destroy the city if there were 50 righteous people in it, or 45, or 30, 20, even 10 righteous people. (Abraham's nephew Lot had been living in Sodom.)
Some time after the birth of Isaac, Abraham was commanded by God to offer his son up as a sacrifice in the land of Moriah. Proceeding to obey, he was prevented by an angel as he was about to sacrifice his son, and slew a ram which he found on the spot. As a reward for his obedience he received another promise of a numerous seed and abundant prosperity (22). Thence he returned to Beersheba. The near sacrifice of Isaac is one of the most challenging, and perhaps ethically troublesome, parts of the Bible.
The primary interest of the narrative now turns to Isaac. To his "only son" (22:2, 12) Abraham gave all he had, and dismissed the sons of his concubines to the lands outside Palestine; they were thus regarded as less intimately related to Isaac and his descendants (25:1-6). See also: Midianites, Sheba.
Sarah died at an old age, and was buried in the cave of Machpelah near Hebron, which Abraham had purchased, along with the adjoining field, from Ephron the Hittite (Genesis 23). Here Abraham himself was buried. Centuries later the tomb became a place of pilgrimage and the traditional site was later marked by an Islamic mosque.