We describe the target selection and resulting properties of a spectroscopic sample of luminous, red galaxies (LRG) from the imaging data of the Sloan Digital Sky Survey (SDSS). These galaxies are selected on the basis of color and magnitude to yield a sample of luminous, intrinsically red galaxies that extends fainter and further than the main flux-limited portion of the SDSS galaxy spectroscopic sample. The sample is designed to impose a passively-evolving luminosity and rest-frame color cut to a redshift of 0.38. Additional, yet more luminous, red galaxies are included to a redshift of 0.5. Approximately 12 of these galaxies per square degree are targeted for spectroscopy, so the sample will number over 100,000 with the full survey. SDSS commissioning data indicate that the algorithm efficiently selects luminous (M_g=-21.4), red galaxies, that the spectroscopic success rate is very high, and that the resulting set of galaxies is approximately volume-limited out to z=0.38. When the SDSS is complete, the LRG spectroscopic sample will fill over 1h^-3 Gpc^3 with an approximately homogeneous population of galaxies and will therefore be well suited to studies of large-scale structure and clusters out to z=0.5.
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