Abstract: Both forward and inverse formulas between auxiliary and geodetic latitudes are derived with the help of computer algebra system in a comprehensive way;and also some mistakes that once were made in the high orders of previous forward formulas are pointed out and corrected.New symbolic expressions of the inverse expansions for these auxiliary latitudes are systematically given in virtue of Hermite interpolation.Their coefficients are expressed in a power series of the eccentricity e,which makes the expansions more uniform.