The study investigates the size distribution of galaxies in the Sloan Digital Sky Survey (SDSS), focusing on how this distribution varies with luminosity, stellar mass, and morphological type. Using a sample of about 140,000 galaxies, the research finds that the size distribution of galaxies at a given luminosity or stellar mass is well described by a log-normal function, characterized by its median size $ \bar{R} $ and dispersion $ \sigma_{\ln R} $. For late-type galaxies, a characteristic luminosity $ M_{r,0} \sim -20.5 $ (assuming h = 0.7) corresponds to a stellar mass $ M_0 \sim 10^{10.6} M_{\odot} $. Galaxies more massive than $ M_0 $ have $ \bar{R} \propto M^{0.4} $ and $ \sigma_{\ln R} \sim 0.3 $, while less massive galaxies have $ \bar{R} \propto M^{0.15} $ and $ \sigma_{\ln R} \sim 0.5 $. For early-type galaxies, the $ \bar{R} - M $ relation is steeper, $ \bar{R} \propto M^{0.55} $, but the $ \sigma_{\ln R} - M $ relation is similar to that of bright late-type galaxies. Faint red galaxies have sizes independent of their luminosity. The results are interpreted using theoretical models, showing that the observed $ \bar{R} - M $ relation for late-type galaxies aligns with predictions from the standard feedback model. The $ \sigma_{\ln R} - M $ relation requires that the bulge/disk mass ratio be larger in haloes of lower angular momentum and that the bulge material transfer part of its angular momentum to the disk. For early-type galaxies, the $ \sigma_{\ln R} - M $ relation is inconsistent with formation through single major mergers but consistent with repeated mergers. The study also finds that the size distribution of galaxies depends on their stellar mass, with early-type galaxies showing a steeper $ \bar{R} - M $ relation. The surface-brightness distribution is found to be normal for a given luminosity, with bright late-type galaxies having systematically higher surface-brightness, consistent with the Kormendy relation. The results provide insights into galaxy formation and evolution.The study investigates the size distribution of galaxies in the Sloan Digital Sky Survey (SDSS), focusing on how this distribution varies with luminosity, stellar mass, and morphological type. Using a sample of about 140,000 galaxies, the research finds that the size distribution of galaxies at a given luminosity or stellar mass is well described by a log-normal function, characterized by its median size $ \bar{R} $ and dispersion $ \sigma_{\ln R} $. For late-type galaxies, a characteristic luminosity $ M_{r,0} \sim -20.5 $ (assuming h = 0.7) corresponds to a stellar mass $ M_0 \sim 10^{10.6} M_{\odot} $. Galaxies more massive than $ M_0 $ have $ \bar{R} \propto M^{0.4} $ and $ \sigma_{\ln R} \sim 0.3 $, while less massive galaxies have $ \bar{R} \propto M^{0.15} $ and $ \sigma_{\ln R} \sim 0.5 $. For early-type galaxies, the $ \bar{R} - M $ relation is steeper, $ \bar{R} \propto M^{0.55} $, but the $ \sigma_{\ln R} - M $ relation is similar to that of bright late-type galaxies. Faint red galaxies have sizes independent of their luminosity. The results are interpreted using theoretical models, showing that the observed $ \bar{R} - M $ relation for late-type galaxies aligns with predictions from the standard feedback model. The $ \sigma_{\ln R} - M $ relation requires that the bulge/disk mass ratio be larger in haloes of lower angular momentum and that the bulge material transfer part of its angular momentum to the disk. For early-type galaxies, the $ \sigma_{\ln R} - M $ relation is inconsistent with formation through single major mergers but consistent with repeated mergers. The study also finds that the size distribution of galaxies depends on their stellar mass, with early-type galaxies showing a steeper $ \bar{R} - M $ relation. The surface-brightness distribution is found to be normal for a given luminosity, with bright late-type galaxies having systematically higher surface-brightness, consistent with the Kormendy relation. The results provide insights into galaxy formation and evolution.