Satan means "the adversary". I'll list some possible interpretations of Satan (either as a title/symbol or even as an entity). This page is work in progress so this is merely a quick draft for now.
Mythological sources:
1: The Bible
2: The Quran
3: Romantic Literature (e.g. Paradise Lost by John Milton)
4: Anton Lavey's Satanic Bible
5: others??? (I may add more)
Meanings:
1: Abrahamic concept of evil i.e. whatever goes against the ideas of Yahweh/Allah
1.1: a subset of this, for pragmatic reason, may focus more as an opposition of the violent ideas found in Christianity and Islam, or as a promotion of hedonism and indulgence (both sexual and non-sexual) with the caveat of restraining oneself from harming others.
1.2: Harming others is okay too if it allows you to reach your goals, though unlike #2 harming others should never be the goal in and of itself (Machiavellian?).
2: Secular concept of evil i.e. intentionally inflicting harm upon others (popularized by horror movies???)
3: Adversarial in the sense of stopping and sabotaging a group of people, or an ideology
4: (if my understanding is correct, etymologically deriving from Latin "adversus", though I'm not sure whether this meaning was found in the original Hebrew word "ha-Satan", "the adversary") Adversarial in the sense of "adding" new, contradictory perspectives into a belief system, though the original belief can be retained if the new one is not convincing enough. Satan in this sense can be tought as a Muse or as a teacher of knowledge. This interpretation is corroborated by both Christian and Islamic teachings, e.g. the Serpent in the Garden of Eden who added the idea of the possibility that Yahweh was lying to them when he (Yahweh) told Adam and Eve not to eat the forbidden fruit (which became an apple likely due to a calque from the Latin word "malum" which meant both "evil" and "apple"), and the idea that Satan whispers in your ears to make you doubt that Islam is the only "true" religion. In both cases it's an addition of oppositional ideas that may (or may not) make one question their previous beliefs. This will be explored further even in a psychological sense, with confirmation bias, Semmelweis reflex, anchoring effect etc. In this interpretations, Satan (when understood as an entity) can:
4.1: work on the side of the Abrahamic deity to "test" the faith of Abrahamic people (though that would necessarily imply that the Abrahamic deity is not omniscient), or
4.2: can work against the Abrahamic deity, with the goal of reducing the number of followers of Abrahamic religions: in this case, Satan's priority isn't to gain followers for himself/herself/etc. but to reduce the number of followers of Yahweh/Allah, so the existence of atheistic Satanism is perfectly coherent under this narrative.
Reasoning 1: whatever you believe in, Satan always adds contradictory ("adversarial") points of view for you to consider. This means, Satan teaches all points of view (including Christianity and Islam, especially if you dislike those two worldviews).
Reasoning 2: some highly sectarian and conservative Christians call anything that they disagree with (including other denominations of Christianity) "Satanic". Since there are at least two denominations of Christianity whose members have that kind of behavior in relatively large frequencies, it follows that all points of view, religions, philosophies, worldviews etc. are Satanic, no exception. Which means, all beliefs and knowledge comes from Satan.
Possible implication of "Satan as the teacher of all knowledge": the very act of having a worldview, beliefs, following a religion/political ideology/etc. is "Satanic" ("adversarial"), in the sense that it "goes against nature". If one sees the species Homo Sapiens (i.e. humans) as "unnatural" (as opposed to other animal species who may be seen as more "natural"), the idea that having a worldview is "adversarial" may provide further confirmation to the idea that humans are "unnatural". If one desires to be more "natural", then, they can try to get rid of any worldview or belief they have, though it is unclear how they'd actually go on and do it, or whether that's even possible.
Arguments against the idea that Satan is the teacher of all knowledge may be coming soon...