The Islamic theology of Satan runs like this: After creating Adam, God commands all to bow before Adam. Satan, one of the Jinn (genies) (Qur'an 18:50) refuses because he was made from fire, while humans are only made from clay (7:10-18, 15:26-39, 17:61-63, 18:50, 20:115-123). The argument doesn't make any sense, but, rather than re-educate Satan, God decides that a more useful course of action is to condemn Satan forever. Satan asks permission to cause evil for others and to lead them astray (e.g., 15:39), and rather than keep peace in the Universe and protect humanity from this powerful foe, God goes for it. The whole story is stated in 7:10-27, again in 15:26-46 and again in 20:115-124; and a shorter version in 17:61-63. In a world where many have been killed people 'following orders', we have all learnt to question instructions, but Satan and the Jinn were treated remorselessly, punished for an infinite period of time for an action that was not even a moral concern (the same happens to Adam and Eve in the Bible). In the modern world where we expect justice and morality to be embodied by the divine, the Quranic story of Shaitan is very difficult to accept and it portrays God as the enabler of arbitrary evil rather than as a protector of humankind.
In Islam Shaitan can be used to describe any barrier or opposition to God, no matter its intention. The formal name of the being that represents all such attempts is Iblis. It is safe to assume that wherever you see Shaitan capitalized as Shaitan, then, it is in fact a reference to Iblis but Shaitan is often easier to use because of its similarity to Satan.
Satan and the jinn were not rejected for any action that was immoral, but for their questioning of a divine command. Satan represents freethought, intelligence, truth-seeking and doubt, which are all strictly forbidden by God. This has parallels with the Christian concept of the Tree of Knowledge in the Garden of Eden: Believe the wrong things, or, be tricked, and you will be punished severely and eternally! The God of Islam and Christianity is a true monster.
In Islam a Muslim must always seek to worship the creator, Allah, and not the creation (the material world). The worship of material things is the utmost evil. Satan represents materialism, truth-seeking and intelligence, three of the greatest enemies of the Islamic God.
Satan in Islam is a surprisingly slippery fellow, and it is hard to discern what part he plays in the formal theology of Islam, where the power and justice of God is emphasized so heavily at the price of any other powerbase that Satan can only ever operate purely under the permission of Allah. This is highlighted by verses that denigrate Satan and portray him as not even very clever:
“Satan's cunning is weak indeed ... The true believers fight for the cause of God, but the infidels fight for the devil. Fight then against the friends of Satan. Satan's cunning is weak indeed.'”
How can such a being manage to defy God? Given that all-powerful nature of God it is clear that Satan and God are interchangeable; they're two faces of the same divinity, except, that the Quran only tells one side of the story.
“At one point Muhammad and his kin were opposed by the polytheists around them. In particular, they were oppressed by the followers of 3 pagan gods in Mecca. When defeated, surrounded and under siege, Muhammad 'seems to have even compromised his monotheism, at first, to make peace with the Meccans'1 and then he suddenly recalled some text that stated that the three pagan gods were valid intercessors after verses 19 and 20 (see how it reads now: Qur'an 53:10-12,18-23), after all! Lucky for Muhammad he remembered this important fact!
When Muhammad had a powerful army and his exiled followers returned, he recited a further passage: saying that it was an error, the three pagan gods were not valid - that Satan recites his own verses but now that "God annuls what Satan casts" Qur'an 22:52! The same in Qur'an 16:101-103, where it says some verses can be later changed for others by God - and here also, the authors must have known how dodgy it sounds, as it mentions that these abrogations cause people to cry out "you are only a forger!". But how can this be, when Qur'an 39:28 says that the Qur'an is perfect? If it's perfect, it's not possible to update verses with a better version - this can only mean that those verses weren't perfect. Whether it was Muhammad changing things, or Satan, or the Angel Gabrielle himself, it undermines our trust in the entire book. If that insertion was made, but annulled, what others have been made, and left in?”