The term elliptic polynomials refers to the polynomials generated by o dd elliptic integrals and elliptic functions. In studying these, the a uthors consider such things as orthogonality and the construction of w eight functions and measures, finding structure constants and interest ing inequalities, and deriving useful formulas and evaluations. Althou gh some of the material may be familiar, it establishes a new mathemat ical field that intersects with classical subjects at many points. Its wealth of information on important properties of polynomials and clea r, accessible presentation make...