marriage - How widespread is the belief that Adam had a first wife?

I have heard of that the idea that Adam had a wife before Eve comes from Jewish tradition, and also about the idea that this wife was Lilith. From what I can tell the story of Lilith and the story of Adams first wife had possibly been around for a long time before being more popularly believed as the same person. But my questing is how widespread is either belief and to what extent is it believed. In other words are any of these ideas (A. Adam had any first wife at all, B. That wife was named Lilith or C. was the demoness Lilith.) common among the modern Jewish population? and if any of these are common to what extent are they believed? Believed strongly, just an interesting possibility, or even denounced completely as false.