We have obtained a complete orbit of spectroscopy at 2.3 Å resolution on AM Herculis in its low state. We find: <P />1. Strong, sharp Hβ, Hγ, and Hδ lines and weak, sharp He I λλ4471, 4922, and 5015 lines. The He II 4686 line is also weak and sharp. There is no trace of the broad emission component present at high state. The radial velocity amplitude K = 79 km s<SUP>-1</SUP> and fiducial phase φ<SUB>0</SUB> = 0.61 identify the sharp emission as being related to the sharp emission component seen at high state. <P />2. The spectrum is stuffed with broad absorption troughs flanking the Balmer lines. These troughs are 10% deep, 80 Å wide, and vary in strength with orbital phase (being strongest at φ<SUB>mag</SUB> = 0.6). The troughs show internal structure and are identified as being Zeeman-shifted multiplets of Hβ, Hγ, and Hδ seen in a magnetic field of 1.3 × 10<SUP>7</SUP> gauss. The trough structure allows us to place a limit of 106 gauss in the variation of the magnetic field in the absorption region. This suggests the lines arise from the accreting polar cap of the white dwarf. <P />3. Lower resolution (13 A) spectra in the red show strong, narrow Hα emission. The energy distribution rises sharply longward of 6500 Å, and there are broad, deep TiO bands from the M4.5 V red dwarf in the binary system. The Zeeman components of Hα are confused with some of these TiO bands.