Data of our compiled catalog containing the positions, velocities, and metallicities of 415 RR Lyrae variable stars and the relative abundances [el/Fe] of 12 elements for 101 RR Lyrae stars, including four {alpha} elements (Mg, Ca, Si, and Ti), are used to study the relationships between the chemical and spatial-kinematic properties of these stars. In general, the dependences of the relative abundances of {alpha} elements on metallicity and velocity for the RR Lyrae stars are approximately the same as those for field dwarfs. Despite the usual claim that these stars are old, among them are representatives of the thin disk, which is the youngest subsystem of the Galaxy. Attention is called to the problem of low metallicity RR Lyrae stars. Most RR Lyrae stars that have the kinematic properties of thick disk stars have metallicities [Fe/H]<-1.0 and high ratios [{alpha}/Fe]~=0.4, whereas only about 10% of field dwarfs belonging to the so-called "low-metallicity tail" have this chemical composition. At the same time, there is a sharp change in [{alpha}/Fe] in RR Lyrae stars belonging just to the thick disk, providing evidence for a long period of formation of this subsystem. The chemical compositions of SDSS J1707+58, V455 Oph, MACHO176.18833.411, V456 Ser, and BPS CS 30339-046 do not correspond to their kinematics. While the first three of these stars belong to the halo, according to their kinematics, the last two belong to the thick disk. It is proposed that they are all most likely extragalactic, but the possible appearance of some of them in the solar neighborhood as a result of the gravitational action of the bar on field stars cannot be ruled out.