This paper presents the detailed abundances and r-process classifications of 126 newly identified metal-poor stars as part of an ongoing collaboration, the R-Process Alliance. The stars were identified as metal-poor candidates from the RAdial Velocity Experiment (RAVE) and were followed-up at high spectral resolution (R~31,500) with the 3.5~m telescope at Apache Point Observatory. The atmospheric parameters were determined spectroscopically from Fe I lines, taking into account <3D> non-LTE corrections and using differential abundances with respect to a set of standards. Of the 126 new stars, 124 have [Fe/H]<-1.5, 105 have [Fe/H]<-2.0, and 4 have [Fe/H]<-3.0. Nine new carbon-enhanced metal-poor stars have been discovered, 3 of which are enhanced in r-process elements. Abundances of neutron-capture elements reveal 60 new r-I stars (with +0.3<=[Eu/Fe]<=+1.0 and [Ba/Eu]<0) and 4 new r-II stars (with [Eu/Fe]>+1.0). Nineteen stars are found to exhibit a `limited-r signature ([Sr/Ba]>+0.5, [Ba/Eu]<0). For the r-II stars, the second- and third-peak main r-process patterns are consistent with the r-process signature in other metal-poor stars and the Sun. The abundances of the light, alpha, and Fe-peak elements match those of typical Milky Way halo stars, except for one r-I star which has high Na and low Mg, characteristic of globular cluster stars. Parallaxes and proper motions from the second Gaia data release yield UVW space velocities for these stars which are consistent with membership in the Milky Way halo. Intriguingly, all r-II and the majority of r-I stars have retrograde orbits, which may indicate an accretion origin.
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