The Church of Satan does not believe in Satan, and that is not a technicality or a modern softening. It is the position the organisation was founded on and has held without deviation ever since.
Anton LaVey founded it in San Francisco on the night of 30 April 1966, Walpurgisnacht, chosen for effect. Its philosophy, set out in The Satanic Bible of 1969, is materialist: there is no god, no devil and no supernatural order, the universe is indifferent, and a person's obligations run to themselves and to those they choose. Satan is a symbol (the adversary, the accuser, the figure who refuses to kneel), standing for pride, self-interest, indulgence rather than abstinence, and the rejection of what the Church regards as the herd morality of Christianity. Its current High Priest, Peter Gilmore, has described members as sceptical atheists and put the position bluntly: Satanism begins with atheism.
The intellectual sources are visible and were never concealed: Nietzsche, Ayn Rand, social Darwinism, the carnival, and a great deal of theatre. Ritual exists, and the Church describes it frankly as psychodrama: a technique for working on oneself, not a petition addressed to anything.
The distinction between this and devil worship matters, because a great deal of what was done to people in the name of stopping devil worship was done on the assumption that no such distinction exists.
LaVey's own biography was substantially embroidered (the circus, the police photography, the celebrated affair), and the Church has never much minded, on the view that a good story is a legitimate instrument and that its philosophy stands or falls independently.