Terahertz time-domain spectroscopy (THz-TDS) is a unique technique for characterizing the response of materials and devices in the far-infrared region of the electromagnetic spectrum. Based on the measurement of transmitted or reflected ultra-short electromagnetic pulses and on a Fourier-transform of the recorded waveforms, THz-TDS permits fast and precise determination of the permittivity or permeability of materials over a wide bandwidth. This book is devoted to the determination of this spectral response of samples from the recorded waveforms.