Our studies to this point have been concerned almost entirely with points, lines, and circles. Here we turn to more general curves, but only those given by polynomials. These are algebraic curves. This is a brief introduction to a vast subject: We keep our scope modest, and our goal simple and clearly defined. We confine our attention to algebraic plane curves, that is, curves given by the zero sets associated to polynomials over \(\mathbb R\) in two variables. Our goal is to appreciate Bézout’s Theorem for plane curves, one of the cornerstones of the subject.