The Sloan Digital Sky Survey (SDSS) selects a main galaxy sample for spectroscopy using a photometric algorithm based on the Petrosian magnitude system. This system measures galaxy flux in apertures determined by the surface brightness profile, making it independent of cosmological dimming, foreground extinction, and sky brightness. The main galaxy sample includes galaxies with r-band Petrosian magnitude $ r \leq 17.77 $ and surface brightness $ \mu_{50} \leq 24.5 $ magnitudes per square arcsec, resulting in about 90 galaxy targets per square degree with a median redshift of 0.104. The algorithm effectively separates stars from galaxies, with less than 0.5% of true galaxies rejected. The sample is highly complete (exceeding 99%), and the selection is reproducible, consistent with photometric errors. The main cause of incompleteness is blending with saturated stars, which affects brighter galaxies more. The SDSS spectra have a high signal-to-noise ratio (S/N > 4 per pixel), ensuring reliable redshift measurements for 99.9% of targeted galaxies. About 6% of galaxies that meet the selection criteria are not observed due to fiber separation limits, but these can be accounted for in statistical analyses. The uniformity and completeness of the sample make it ideal for studying large-scale structure and galaxy properties in the local universe. The algorithm uses a modified Petrosian magnitude system, with galaxies selected in the r-band. The Petrosian radius and half-light surface brightness are defined based on the galaxy's surface brightness profile. The algorithm is tested for its performance, showing that it meets the survey's requirements for completeness, uniformity, and reproducibility. The selection process includes a star-galaxy separation, surface brightness limits, and fiber assignment, ensuring that only galaxies meeting specific criteria are targeted. The algorithm is also tested for its spectroscopic characteristics, showing that the sample has high S/N and reliable redshift measurements. The final selection includes galaxies with fiber magnitudes brighter than 19.0, ensuring that most targeted galaxies have sufficient S/N for redshift measurement. The algorithm is designed to minimize contamination from stars and ensure that the sample is representative of the galaxy population. The SDSS spectroscopic survey targets a wide range of galaxies, including luminous red galaxies (LRGs), and the main galaxy sample is used for large-scale structure studies. The algorithm is optimized for efficiency, with a tiling algorithm that assigns galaxies to spectroscopic plates in a way that maximizes observing efficiency. The final selection includes galaxies with a minimum surface brightness and fiber magnitude, ensuring that the sample is complete and representative. The algorithm is validated through various tests, showing that it meets the survey's requirements for completeness, uniformity, and reproducibility. The SDSS galaxy sample is ideal for studying large-scale structure and galaxy propertiesThe Sloan Digital Sky Survey (SDSS) selects a main galaxy sample for spectroscopy using a photometric algorithm based on the Petrosian magnitude system. This system measures galaxy flux in apertures determined by the surface brightness profile, making it independent of cosmological dimming, foreground extinction, and sky brightness. The main galaxy sample includes galaxies with r-band Petrosian magnitude $ r \leq 17.77 $ and surface brightness $ \mu_{50} \leq 24.5 $ magnitudes per square arcsec, resulting in about 90 galaxy targets per square degree with a median redshift of 0.104. The algorithm effectively separates stars from galaxies, with less than 0.5% of true galaxies rejected. The sample is highly complete (exceeding 99%), and the selection is reproducible, consistent with photometric errors. The main cause of incompleteness is blending with saturated stars, which affects brighter galaxies more. The SDSS spectra have a high signal-to-noise ratio (S/N > 4 per pixel), ensuring reliable redshift measurements for 99.9% of targeted galaxies. About 6% of galaxies that meet the selection criteria are not observed due to fiber separation limits, but these can be accounted for in statistical analyses. The uniformity and completeness of the sample make it ideal for studying large-scale structure and galaxy properties in the local universe. The algorithm uses a modified Petrosian magnitude system, with galaxies selected in the r-band. The Petrosian radius and half-light surface brightness are defined based on the galaxy's surface brightness profile. The algorithm is tested for its performance, showing that it meets the survey's requirements for completeness, uniformity, and reproducibility. The selection process includes a star-galaxy separation, surface brightness limits, and fiber assignment, ensuring that only galaxies meeting specific criteria are targeted. The algorithm is also tested for its spectroscopic characteristics, showing that the sample has high S/N and reliable redshift measurements. The final selection includes galaxies with fiber magnitudes brighter than 19.0, ensuring that most targeted galaxies have sufficient S/N for redshift measurement. The algorithm is designed to minimize contamination from stars and ensure that the sample is representative of the galaxy population. The SDSS spectroscopic survey targets a wide range of galaxies, including luminous red galaxies (LRGs), and the main galaxy sample is used for large-scale structure studies. The algorithm is optimized for efficiency, with a tiling algorithm that assigns galaxies to spectroscopic plates in a way that maximizes observing efficiency. The final selection includes galaxies with a minimum surface brightness and fiber magnitude, ensuring that the sample is complete and representative. The algorithm is validated through various tests, showing that it meets the survey's requirements for completeness, uniformity, and reproducibility. The SDSS galaxy sample is ideal for studying large-scale structure and galaxy properties