Clusters of galaxies are the most massive gravitationally bound systems in the Universe. They have been extensively used as efficient probes of large-scale structure and ideal laboratories to study galaxy population and evolution. In this thesis I present an adaptive matched-filter algorithm designed to identify clusters of galaxies from current and future wide-field multi-band optical surveys. The technique is fully adaptive in 2-D, 2.5-D and 3-D cases, and responsive to different cluster scales, colors, and substructures. The cluster-finding algorithm is then applied to the Sloan Digital Sky Survey data, resulting in two samples of optically selected galaxy clusters. The DR6 ("wide") catalog includes 69,173 clusters extracted from the SDSS single-epoch main survey covering 9,600 square degrees of the sky across the redshift range of 0.05 z 0.78. Tests against realistic mock SDSS catalogs from large N-body dark matter simulations suggest that the selected cluster sample is ∼ 85% complete and over 90% pure for systems more massive than 1.0 x 1014h -1 M⊙ with redshifts up to z = 0.45. It is also cross-matched and compared with other recent optical cluster samples and X-ray detections, with clear correlation found in scaling relations among various observables. The Stripe 82 ("deep") catalog contains 9,975 clusters of galaxies from the the co-added imaging data in the ∼ 275 deg2 SDSS Southern Stripe centered on the Celestial Equator, spanning the redshift range of 0.05 ≤ z 1.2. The cluster sample is found to be nearly volume-limited to redshift z ∼ 0.8 - 0.9, and represents one of the deepest optical cluster catalogs that have ever been built with such decent sky coverage. With masses properly calibrated through weak gravitational lensing, the two cluster samples can be used supplementary to each other and greatly enhance our understanding of various aspects of cluster science and their implications for astrophysics and cosmology.
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