  We analyze the high-resolution X-ray spectrum of Hercules X-1, an
intermediate-mass X-ray binary, which was observed with the XMM-Newton
Reflection Grating Spectrometer. We measure the elemental abundance ratios by
use of spectral models, and we detect material processed through the CNO-cycle.
The CNO abundances, and in particular the ratio N/O > 4.0 times solar, provide
stringent constraints on the evolution of the binary system. The low and
short-on flux states of Her X-1 exhibit narrow line emission from C VI, N VI, N
VII, O VII, O VIII, Ne IX, and Ne X ions. The spectra show signatures of
photoionization. We measure the electron temperature, quantify photoexcitation
in the He alpha lines, and set limits on the location and density of the gas.
The recombination lines may originate in the accretion disk atmosphere and
corona, or on the X-ray illuminated face of the mass donor (HZ Her). The
spectral variation over the course of the 35 d period provides additional
evidence for the precession of the disk. During the main-on state, the narrow
line emission is absent, but we detect excesses of emission at ~10--15 A, and
also near the O VII intercombination line wavelength.
