  A class of rational functions characterized by some wonderful properties is
studied. The properties that identify this class include simple algebra (their
inverses can be expressed in radicals), simple topology (the total space of the
minimal Galois covering dominating them has genus 0 or 1) and simple local
topol- ogy (branching data). Explicit formulae for these functions are obtained
as well as their classification up to different equivalence relations.
