We present the first observations of a Herbig Ae star with a circumstellar disk by the Far-Ultraviolet Spectroscopic Explorer (FUSE) as well as a simultaneous observation of the star obtained with the Hubble Space Telescope/Space Telescope Imaging Spectrograph (STIS). The spectra of AB Aurigae show emission and absorption features arising from gases that have a wide range in temperature, from hot O VI emission to cold H2 and CO absorption. Emissions from the highly ionized species O VI and C III present in the FUSE spectrum are redshifted, while absorption features arising from low-ionization species like O I, N I, and Si II are blueshifted and show characteristic stellar wind line profiles. We find that the total column density of H2 toward AB Aur from the FUSE spectrum is N(H2) = (6.8 ± 0.5) × 1019 cm-2. The gas kinetic temperature of the H2 derived from the ratio N(J = 1)/N(J = 0) is 65 ± 4 K. The column density of the CO observed in the STIS spectrum is N(CO) = (7.1 ± 0.5) × 1013 cm-2, giving a CO/H2 ratio of (1.04 ± 0.11) × 10-6. We also use the STIS spectrum to find the column density of H I, which permits us to calculate the total column density of hydrogen atoms, the fractional abundance of H2, and the gas-to-dust ratio.