We have analyzed the ROSAT PSPC observations of the central region of the Fornax cluster, a relatively poor group of galaxies at a distance of about 24 Mpc. The brightest X-ray and optical galaxy in the group is NGC 1399, an E1 galaxy located near the center of the Fornax cluster. We characterize the hot gas around the galaxy, derived from a 2' to 18' annulus around NGC 1399, as having a mean temperature of 1.30 ± 0.05 keV and a heavy element abundance of 0.6 ± 0.1 with respect to solar abundance (Fe/H = 4.68 × 10-5 by number). Spatially resolved spectral data provide both gas temperature and gas abundance profiles extending to 125 kpc (18') from the galaxy. The temperature distribution, combined with the X-ray surface brightness profile, yields an accurate determination of the gravitating mass within 125 kpc, which falls in the range (4.3-8.1) × 1012 M☉ (95% confidence range, including systematic uncertainties). If we include the extended optical halo around NGC 1399, the mass-to-light ratio increases with radius from 33 ± 8 M☉/L☉ at 18 kpc to 70 ± 22 M☉/L☉ at 110 kpc. We compare the heavy element abundance distribution measured around NGC 1399 with that measured around the Virgo galaxy NGC 4472, as well as to models for hot coronae. We find that the abundance distribution is in good agreement with that previously measured for NGC 4472 by Forman et al. in 1993. For both galaxies, the observed abundance profiles require both a weak evolution of the type Ia supernova rate with time and a present epoch rate which agrees with that of Cappellaro et al. We compare mass measurements in NGC 1399 to those for M87. The similarity of the optical masses in these systems and their differences in gas masses and gravitating masses lead us to suggest that the optical galaxies formed at an early stage when the central potentials of these two systems were similar. Subsequent infall of gas and dark matter into the larger, deeper Virgo potential resulted in the greater mass of the Virgo cluster compared to Fornax. We also report on X-ray properties of thirteen other Fornax galaxies. Eight of these were detected in ROSAT images with luminosities in the 0.2 to 2 keV energy band from 1 × 1039 to 1.6 × 1041 ergs s-1. Five galaxies were sufficiently bright to permit spectral analyses and all but one (NGC 1380) had spectra consistent with thermal emission. Two (NGC 1404 and NGC 1387) of the four galaxies with well-constrained spectral parameters have hot coronae with characteristic gas temperatures of about 0.5 keV and iron abundances less than that found around NGC 1399 and other bright ellipticals. To maintain these hot coronae, the absolute magnitudes of these galaxies must be brighter than -19. Thus the distance to Fornax must be at least 18 Mpc, and, if there are no large peculiar velocities, the Hubble constant should be less than 75 km s-1 Mpc-1. Since these galaxies are all members of Fornax, distance uncertainties do not affect the relationship between their optical magnitude and X-ray luminosity. Analysis of the Fornax galaxies supports the contention that the scatter in the X-ray and optical relationship is intrinsic and does not arise solely from distance uncertainties. For the elliptical galaxy NGC 1404, the X-ray images show that the hot corona is distorted and likely is being stripped, indicating infall of the galaxy toward NGC 1399 and the cluster center.