Spectia of sixty-seven H Ir regions from 3 to 24 kpc from the nucleus of M31 have been obtained with the DTM image-tube spectrograph at a dispersion of 135 A mm '. Radial velocities, principally from Ha, have been determined with an accuracy of 10 km sec ' for most regions. Rotational velocities have been calculated under the assumption of circular motions only. For the region interior to 3 kpc where no emission regions have been identified, a narrow [N 13] x6583 emission line is observed. Velocities from this line indicate a rapid rotation in the nucleus, rising to a maximum circular velocity of V = 225 km at R = 400 pc, and falling to a deep minimum near R = 2 kpc. From the rotation curve for R < 24 kpc, the following disk model of M31 results. There is a dense, rapidly rotating nucleus of mass Al = (6 i 1) x 10' Alo. Near R = 2 kpc, the density is very low and the rotational motions are very small. In the region from 500 to 1.4 kpc (most notably on the southeast minor axis), gas is observed leaving the nucleus. Beyond R = 4 kpc the total mass of the galaxy increases approximately linearly to R = 14 kpc, and more slowly thereafter. The total mass to R = 24 kpc is = (1 85 t 0.1) x 10" Alo; one-half of it is located in the disk interior to R = 9 kpc In many respects this model resembles the model of the disk of our Galaxy Outside the nuclear region, there is no evidence for noncircular motions. The optical velocities, R > 3 kpc, agree with the 21-cm observations, although the maximum rotational velocity, V = 270 t 10 km sec ', is slightly higher than that obtained from 21-cm observations.