The technique of frequency-modulation enhanced magnetic rotation spectroscopy (FM-MRS) is described. An experimental comparison between FM-MRS, frequency-modulation, and magnetic rotation spectroscopies clearly demonstrates that the double null absorption-based FM-MR technique is more sensitive than either FM or MRS separately. The theoretical basis for this sensitivity enhancement can be attributed to a 1/theta (where theta is the small uncrossing angle between two nearly crossed polarizers) improvement in the sensitivity of the combined FM-MR technique relative to that of standard FM spectroscopy. The sensitivity improvement of FM-MRS relative to MRS is even better than that for FM spectroscopy. In practical terms, this enhancement can improve the experimentally achievable sensitivity of FM and magnetic rotation spectroscopies by factors of O(10(1)) to O(10(2)) and O(10(2)) to O(10(4)), respectively, levels that approach the theoretical quantum noise limit. In addition, because FM-MRS is based on the Zeeman effect, Zeeman information is encoded into FM-MR line profiles in the form of relative phase labels and line shapes. The relative phases and line shapes of rotational lines can be used to group features by rotational branch and to differentiate between magnetically active (Lambda not equal 0, Sigma not equal 0) and inactive (Lambda=0, Sigma=0) features. The theory of FM-MRS, including a discussion of line shapes and a sensitivity analysis, is reviewed here; applications of the FM-MR technique are presented separately in the following paper.