Hi, guys. This is an interesting discussion you have going here. But I noticed that many seem to be confused over what Satanism is, so maybe I can help?
There's 2 or 3 main branches of Satanism, from what I can see:
The first branch would be LaVeyan Satanism. This is the system formulated by Anton LaVey in the 1960s, most notably in the Satanic Bible and as taught and practiced by the Church of Satan, which he founded. It is an entirely materialistic philosophy based on Self-worship and carnal gratification. Officially, LaVeyan Satanists don't believe in a spiritual reality nor an afterlife. They only believe in and focus on the here and now. When it comes to atheism, I suppose they would fit the definition in that they don't believe in any external deities. They believe that all deities are the creation of humanity. They use Satan as a symbol of individualism, freedom and rebellion but don't believe in a literal Satan.
LaVeyan Satanism focuses on Nietzschean philosophy and 19th-century "might is right" Social Darwinistic ideals. LaVey also took a lot from Ayn Rand's philosophy. He even said once that his Satanism was basically Ayn Rand's philosophy with ritual thrown in.
Yes, they go practice a form of ritual magick, but they don't view it as a spiritual exercise. They view it as a psychological drama that fulfills a need that the primitive part of us has for ritual and dogma.
To learn more:
Welcome to the Church of Satan
Satanism: An interview with Church of Satan High Priest Peter Gilmore - Wikinews, the free news source
The second main branch are Symbolic or Archetypal Satanists. They basically believe that Satan is a symbol or an archetype that exists within our psyche. They may or may not be influenced by LaVeyan Satanist concepts.
The third main branch is Theistic Satanism (which is where I personally belong). These are the people who view Satan as a literal force, power or being. They may be monotheists, pantheists, duotheists or polytheists. There's no limit to how many disparate views of what/who Satan is in Theistic Satanism. It depends entirely on the prerogative of the individual. Most of us tend to identify Satan with an earlier pre-Christian deity such as Prometheus, Set, Ea, Enki, Pan, Tiamat, Leviathan, Lucifer, etc. There's even groups that link Satan to pantheistic Vedic concepts.
To learn more about Theistic Satanism:
Theistic Satanism: Diane Vera on today's new kinds of Satanists
Pantheistic Satanism:
Dark Doctrines, Left Hand Path and Satanism
A pretty controversial group, but theistic nonetheless:
Order of Nine Angles - The Sinister Tradition
There are also Gnostic Satanists such as the Temple of the Black Light. They are extreme Gnostics who await the destruction of the physical universe so that their souls may be freed into the realm of Pandimensional Chaos. You can learn more about them here:
http://anti-cosmos.orgfree.com/download/Temple-of-The-Black-Light.pdf
General information:
https://en.wikipedia.org/wiki/Satanism
https://en.wikipedia.org/wiki/Theistic_Satanism
Anyway, hope that helps!