Where did the Christian concept of Satan come from? Not from Judaism. Separate concepts in the Jewish tradition are reinterpreted and combined in order to fit into the Christian concept of an arch-enemy working against God.
Ba’al is a rival deity that Yahweh fights and defeats in Jewish mythology. This is the result of the Yahweh worshiping Jews defeating the Ba’al worshiping Jews.
The concept of Lucifer is derived through the misinterpretation of Isaiah 14:9-17. This passage refers to the King of Babylon, a man and not an angel, who was said to seek greatness above God but whose pride was followed by a fall. “Morning Star”—which was translated as Lucifer—was a title given to the King of Babylon in accordance with the belief that he was of divine parentage in association with Venus (the morning star). In Ezekiel 28:12-19 we again find a description that is taken as evidence for a fallen angel but which is originally intended to describe the fall of another earthly king as a result of pride, in this case the King of Tyre.
Azazel is described in two places, not necessarily being the same entity in both. In Leviticus it is a type of demon in the wilderness (either that or a mountain cliff—scholars disagree), to whom a goat is released in addition to the one sacrificed to the lord. In the (apocryphal) book of Enoch, Azazel is a leader of a group of angels known as the Watchers (Grigori). After coming to Earth the Watchers fall in love with human women and bear children by them called the Nephilim, who were a race of giants. Azazel also taught men about weapons and women about cosmetics. The fact that humans had been given divine children was one of the reasons God created the flood, so that his spirit would not remain among them. The flood may also be related to the fact that Yhw(h) may have originally been the god of chaos, destruction, and the stormy sea in the Levantine pantheon.
The Serpent in the Garden of Eden
This was originally taken to be an ordinary serpent (though a speaking one, as is common in fables) and was only later associated by Christians with the concept of Lucifer.
Gary Greenberg, the President of the Biblical Archaeology Society of New York, argues in his book 101 Myths of the Bible that the image of the serpent is taken from the Egyptian concept of Set (the brother and rival of Osiris) in the form of the serpent Aphophis (Re’s enemy who tries to swallow the sun every dusk). This would appear similar to the later Christian concept of Satan, although in the Egyptian context Aphophis arguably represents more an embodiment of primordial chaos against the order of society than an independent order of evil. One could make the argument that Set represented such an order of evil in relation to Osiris, but for that parallel to work Satan would have to have succeeded in his battle against God for God's throne, as Set did against Osiris. And also, Set wasn't considered an entirely negative god. (The complicated relationships among the Egyptian gods were due in no small part to the complicated political relationships among the different Egyptian cities and political powers, each having a different god as their main patron.)
But although the image of the serpent in the garden of Eden may have initially come from an Egyptian context, this may be somewhat besides the point. For within the Biblical context, the story of the serpent in Genesis refers simply to a normal serpent. He is compared to other animals—“more subtle than any beast of the field”—not angels, gods, or demons (Genesis 3:1). And the story of the serpent, like so many other Biblical stories, reads like a fable/myth. Consider the punishments that God doles out in the end of the snake's story, in Genesis 3:14-17:
“And the LORD God said unto the serpent, Because thou hast done this, thou art cursed above all cattle, and above every beast of the field; upon thy belly shalt thou go, and dust shalt thou eat all the days of thy life: And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel. Unto the woman he said, I will greatly multiply thy sorrow and thy conception; in sorrow thou shalt bring forth children; and thy desire shall be to thy husband, and he shall rule over thee. And unto Adam he said, Because thou hast hearkened unto the voice of thy wife, and hast eaten of the tree, of which I commanded thee, saying, Thou shalt not eat of it: cursed is the ground for thy sake; in sorrow shalt thou eat of it all the days of thy life”
This fits in perfectly with the literary motif employed in fables and myths, whereby the world is the way it is because of the actions and encounters of a group's archetypal ancestors: not a coyote but Coyote, not a rabbit but Rabbit, not a Roman but Romulus, etc. Crows are black because Crow was burned by the Fire from the Sun (Lenni Lenape Tribe). Cats purr and are enemies of rats because Rat stole Cat's drum and Cat had to swallow it to keep it safe (African). Echoes are the result of the nymph Echo being cursed to only repeat the words of others as a punishment from Hera for distracting her while Zeus fooled around with the other nymphs (Ancient Greek). The Grand Canyon was formed when Paul Bunyan dragged his axe behind him (19th Century America). Etc.
Some Christians have even gone so far as to suggest that the part about humans bruising the heads of snakes and snakes bruising the heels of humans is a reference to the “enmity” between Satan (the seed of the serpent?) and Christ (Eve's seed). I would hope it would be clear to everyone just how obvious it is that such an interpretation is the result of forcing later meanings onto earlier stories (something Christians have been doing with Biblical stories since there have been Christians), and that this passage in its original context is merely referring to the fact that humans strike the heads of snakes in order to kill them and snakes bite human feet, legs, etc.
The term ha-Satan means literally the-Adversary, and the term is used in a number of contexts that mean adversary in general. The closest thing that we find to the Christian concept is its use as the title (though not the name) assigned to an angel in Yahweh’s court. He was a prosecutor for God against human individuals, with God as the Judge. Ha-Satan could not act without God’s permission and did not cause people to sin, though God may have ha-Satan test a person, as in the case of Job. Ha-Satan’s primary role was to record and point out the sins people committed and argue against them in the holy court in accordance with God’s will. In the (apocryphal) book of Enoch, Satanael/Samyaza is the leader of the Grigori, who again were cast out of heaven for sleeping with human women and producing a race of giants.
In no part of the canonical books of the “Old Testament” are we given the Devil in the Christian sense—the once favored angel that sought to lead a rebellion to overthrow God, was cast from heaven into hell, and now seeks to tempt/trick/torture human beings in opposition to God’s will. Far from Yahweh having created a being that became his adversary, in a number of places, Isaiah 45:7 being one example, Yahweh proclaims that he himself makes both good and evil.
But if the Devil does not come from Judaism, what is its source? Once again, pagan influence. The Zoroastrians believed that there were two gods, one good and one evil, in constant opposition and competition for human souls. Zoroastrianism influenced Judaism during the time period before Christianity arose. The idea of Satan gained influence in Judaism from this intermixing, even producing some apocryphal works like the Book of Enoch that discuss angelic/demonic conflicts, but this was not original to Judaism.
For a more detailed discussion of Zoroastrianism, look here:
Scholar Richard Carrier discusses the relationship between Satan and Christ: