La0.875Sr0.125MnO3 is a mixed-valence manganite that exhibits a variety of nonintuitive many-body phenomena, including anomalous metal-insulator transitions and colossal magnetoresistance. To date, the underlying interactions behind the intriguing behaviors of this material have not been well understood. In this thesis work, we have mapped out the detailed frequency, temperature, and magnetic field dependence of the terahertz (THz) complex optical constants of a single crystal of La0.875Sr0.125MnO3. We revealed a series of novel effects, including simultaneous THz colossal magnetoresistance and magnetocapacitance for the first time. Our results suggest that the percolation theory plays an important role in La0.875Sr0.125MnO3 at temperatures above the charge-ordering temperature. Furthermore, our study provides supporting evidence for a new phase transition at low temperatures whose existence has recently been suggested. Finally, we observed an anisotropic collective excitation, possibly due to the charge density wave in the charge-ordered phase, along the b-axis of the crystal. These results provide considerable new insights into the complex interactions among different degrees of freedom – charge, orbital, spin, and lattice – in La0.875Sr0.125MnO3.