The physics of strongly correlated electronic systems has attracted much attentionrnbecause of its unique and distinct properties like Mott metal-to-insulator transition,rngiant magneto-resistance, superconductivity. While the density functional theoryrn(DFT), the standard approach to electronic band calculations, is able to describernproperties of weakly correlated systems but is known to have serious limitation in therndescription of strongly correlated systems, the dynamical mean field theory (DMFT) hasrnbecome an established method for the treatment of strongly correlated systems. In thisrndissertation, we study the properties of correlated electronic systems near Mott metalto-rninsulator transitions using DMFT, which maps Hubbard like lattice model in infiniterncoordination number to a single site impurity Anderson model with the self-consistentrnconditions. We implement the continuous-time hybridization expansion (CT-HYB)rnversion of continuous-time quantum Monte Carlo (CT-QMC) for the impurity modelrnto investigate the Mott metal-to-insulator in the Hubbard model on Bethe latticernwithout symmetry braking. At half filling a gap opening transition is found to occurrnas the interaction strength is increased beyond critical value. We extend our analysisrnto the inclusion of retarded interaction (electron-phonon interaction) in the framernwork of Hubbard-Holstein model. We implement the CT-HYB in the presence ofrnretarded interaction for the impurity model. The effect of the inclusion of retardedrninteraction to Hubbard model is to shift the Mott metal-to-insulator to a large criticalrnvalues as compared to the pure Hubbard model. The interplay of electron-electron andrnelectron-phonon interaction near the Mott metal-to-insulator transition are discussed