In Gen. 3, we are introduced to the serpent (Hebrew: gahesh). Seemingly, it should be pointed out, gahesh arises from nowhere — in fact, the creature is merely introduced as “more crafty than any of the wild animals the Lord God had made” (Gen. 3:1). (Note: some translations use “subtle” in place of “crafty.”)
There is nothing else introduced about the serpent at all — and throughout the rest of Gen. 3 (he only appears in this chapter) the serpent is only referred to as “the serpent.”
So why is it, then, that everybody thinks it was in fact Satan/Lucifer/The Devil who tempted adam (Hebrew: “man”) and Eve?
There is no textual basis whatsoever for the serpent to be considered one and the same with Satan. The reason: at the time of the oral tradition of this story, no such person existed in Hebrew faith. Satan is actually a Hebrew word, meaning (roughly) “obstruction” or “block.” There’s simply nothing in Genesis to support this etymology — instead, the Hebrew word is nahash, or simply “snake.” “Satan” is an altogether different concept, one that scholar Elaine Pagels has charted.
The association of the serpent with Satan is, actually, through tradition. “Tradition,” when noted regarding Biblical stories, is all too often essentially — in my opinion — a byword for “no textual basis whatsoever.” In this case, the serpent/Satan connection arises entirely not from Genesis, but from the New Testament — in other words, while the Bible contains some textual basis for this assertion, it’s not actually in Genesis, but a much, much later interpretation of Genesis. The Book of Revelation, the last book of the Bible, neatly makes the connection that the Hebrew text does not imply: “that ancient serpent called the devil, or Satan, who leads the whole world astray”(Rev. 20:2).
If you haven’t critically read Gen. 3 yourself — you won’t find anything in there to support a conclusion that gahesh is satan.
Further Reading: The Origin of Satan by Elaine Pagels.