The space defined by mass, radius and velocity dispersion for self-gravitating systems allows a dimension reduction called the Fundamental Plane (FP). These quantities are related through the Virial Theorem. Observationally, the slope of the FP is determined by the relationship between mass and luminosity, more precise the mass-to-light ratio (M/L). In this thesis, we have generated the FP for 6, 132 cluster galaxies as part of a comprehensive program to generate the FP for stellar systems, galaxies, groups, and galaxy clusters. We have also generated a control sample of 4, 423 field galaxies searching for environmental effects that could affect the FP for early-type galaxies. In this study, we have used photometric and spectra measurements from the Sloan Digital Sky Survey Data Release 7 (SDSS-DR7). We have developed an suit of scripts and programs to deal with data selection, cluster membership and galaxy velocity dispersion. We have measured the velocity dispersions of galaxies using two methods: the crosscorrelation method and the direct-line-profile fitting method. We have used the Petrosian radius as a non-parametric scale indicator. The Petrosian radius overcomes the uncertainties of surface brightness profile fitting.