Clusters of galaxies are the largest gravitationally bound systems in the Universe and are located at the knots of cosmic web. They provide powerful constraints on galaxy evolution, the formation of large scale structure of the Universe and many astrophysical processes. This paper summarizes the results we obtained in the last decade on identification of galaxy clusters, studies of the properties of clusters and cluster member galaxies. We developed a method to identify galaxy clusters by using photometric redshifts of galaxies. The method was applied to the survey data of Sloan Digital Sky Survey (SDSS), and we identified 39668 clusters from the sixth data release of SDSS, and later identified 158103 clusters from the twelfth data release of SDSS, which doubles the number of known clusters and extends the redshift range of clusters from 0.3 to 0.8. Recently, we identified 47600 clusters from all sky data of Two Micron All-Sky Survey (2MASS), Wide-field Infrared Survey Explorer (WISE) and SuperCOSMOS, which significantly enlarge the number of clusters outside of the SDSS sky region. More high-redshift clusters were also recently identified from SDSS×WISE and the deep survey data, which significantly enlarge the number of cluster at high redshift. By inspecting the SDSS color images, we found many clusters showing giant arcs, acting as the lensed system for background galaxies. Many following-up studies have been done to understand the properties of galaxy clusters, including their spatial distribution in the Universe, the dynamical state and diffuse radio emission. The two point correlation function of 79091 clusters was calculated to detect the Baryon Acoustic Oscillations (BAO) signal with 3.7σ confidence, which is the first significant detection of the BAO signal by using galaxy clusters as tracers. Based on optical photometric data, we developed a method to quantify the dynamical state of clusters and calculated the relaxation parameter for 2092 rich clusters. We found that the cluster dynamical state is significantly correlated with the absolute magnitude of Brightest Cluster Galaxy (BCG) and also depends on the magnitude difference between the first BCG and the second BCG. The diffuse radio emission of galaxy clsuters detected in merging clusters is related to dynamical state, so that the radio power of diffuse radio emission, cluster mass proxy and dynamical parameters form a fundamental plane. The properties of cluster member galaxies have been investigated in several aspects. By using 2092 clusters with dynamical states, we calculated the composite luminosity function of member galaxies. We found that more relaxed clusters have fewer bright member galaxies, but host a brighter BCG. By cross-matching the largest optical cluster sample with radio data obtained by the Very Large Array (VLA) of National Radio Astronomy Observatory (NRAO) through the NRAO VLA Sky Survey (NVSS) and Faint Images of the Radio Sky at Twenty-centimeters (FIRST), we got the largest complete sample of radio loud BCG. We obtained the radio luminosity function of BCGs, and found that it is related to the optical luminosity of BCG and dynamical state of clusters. BCGs with larger optical luminosity have higher fraction of radio loud. BCGs in more relaxed clusters have higher radio power. It is gareat era now as more deeper sky surveys on many bands are going on. We expect many breakthroughs in the research areas related to galaxy clusters.
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