This is a gonna probably become a huge wall of text regarding Satanism as officially recognized (at least in the UK and US) and defined by Anton LaVey, so if you don't wanna see a huge pile of words, run now

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Satanism is a religion that revlolves around an idea sometimes know as autotheism, i.e. you are your own god. To a Satanist, such as myself, there is no-one more important than the self. This means that the greatest goal in life is to seek whatever will bring you the greatest possible
ultimate pleasure. This differs from hedonism as hedonism follows the philosophy of "eat, drink and be merry, for tomorrow we die", or rather, enjoy yourself know and forget about the consequences of what you do.
Despite the desire for ultimate pleasure, Satanists are often willing to sacrifice something in the short-term to gain greater pleasure over a longer-term basis. As pleasure is both subjective and unquantifiable, this decision on whether or not to sacrifice immediate pleasure is to be judged by the individual Satanist on a case-by-case basis.
As stated previously by Fickel_Pickel, Satanists do not believe in Satan, or in fact any superhuman creature. The term 'Satanism' is merely used because: 1. it shows that our beliefs are antithetical to Christianity, which in the Christian faith is equivocal to following Satan; and 2. It sounds dramtic

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Satanism is theatrical in its nature, not as an inherant part of the philosophy, but partially because it keeps away those who are not truly interested, and partly because revelling in our esoteria is good, harmless fun

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Just for clarity, there are no links between Wicca and Satanism, although I have heard many comments suggesting such a connection.
Hope that wasn't too much, and I really hope it helps to clear things up

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