Terahertz time-domain spectroscopy systems were developed and used for the anaylsis and characterization of various materials. By using ultra-fast Ti:Sapphire and Er-doped fiber lasers, terahertz time-domain spectrometers of different configurations were constructed and tested. To increase the accuracy and sensitivity of the measurements, the systems were optimized for spectroscopic analysis. MBE grown nominally undoped epitaxial GaAs samples were used for the spectroscopic measurements. These samples were first charactrized by electrical measurements in order to check the accuracy of the terahertz time-domain experiments. We have shown that the terahertz time-domin spectroscopic techniques provides a quick way of the determining the real ( ) and complex () components of the refractive index of material. In addition, we have investigated the photoexcitation dynamics of these GaAs samples. We have demonstrated that direct and photoexcited terahertz time-domain measurements give an estimate of the carrier densities and both the hole and electron mobility values with good precision. rnin An algorithm is developed to prevent the unwanted Fabry-Perot reflections which is commonly encountered in Terahertz Spectroscopy systems. We have performed terahertz time-domain transmission measurements on ZnTe &lt / 110&gt / crystals of various thicknesses to test the applicability of this algorithm. We have shown that the algorithm developed provides a quick way of eliminating the &ldquo / etalon&rdquo / reflections from the data. In addition, it is also shown that these &ldquo / etalon&rdquo / effects can be used for the frequency calibration of terahertz time-domain spectrometers.