  The dynamics of all quadratic Newton maps of rational functions are
completely described. The Julia set of such a map is found to be either a
Jordan curve or totally disconnected. It is proved that no Newton map with
degree at least three of any rational function is conformally conjugate to a
unicritical polynomial(i.e., with exactly one finite critical point). However,
there are cubic Newton maps which are conformally conjugate to other
polynomials. The Julia set of such a Newton map is shown to be a closed curve.
It is a Jordan curve whenever the Newton map has two attracting fixed points.
