The terahertz, or far-infrared, region of the electromagnetic spectrum is of critical importance in the spectroscopy of condensed matter systems. The electronic properties of semiconductors and metals are greatly influenced by bound states (e.g., excitons and Cooper pairs) whose energies are resonant with terahertz photons. The terahertz regime also coincides with the rates of inelastic processes in solids, such as tunneling and quasiparticle scattering. As a final example, confinement energies in artificially synthesized nanostruclures, like quantum wells, lie in the terahertz regime. In spite of its importance, terahertz spectroscopy has been hindered by the lack of suitable tools. As pointed out in the introduction to this book, sweptfrequency synthesizers for millimeterand submillimeter-waves are limited to below roughly 100 CHz, with higher frequencies only available using discrete frequency sources. Fourier Transform InfraRed (FTIR) spectroscopy, on the other hand, is hampered by the lack of brightness of incoherent sources. In addition, FTIR methods are not useful if the real and imaginary part of response functions must be measured at each frequency. Terahertz Time-Domain Spectroscopy (THz-TDS) is a new spectroscopic technique that overcomes these difficulties in a radical way. Its advantages have resulted in rapid proliferation within the last few years from a handful of ultrafast laser experts to researchers in a wide range of disciplines. THz-TDS is based on electromagnetic transients generated opto-electronically with the help of femtosecond (lfs = 10 -15 s) duration laser pulses. These THz transients are single-cycle bursts of electromagnetic radiation of typically less than 1 ps duration. Their spectral density spans the range from below 100 GHz to more than 5 THz. Optically-gated detection allows direct measurement of the terahertz electric field with a time resolution of a fraction of a picosecond. From this measurement both the real and imaginary part of the dielectric function of a medium may be extracted, without having to resort to the Kramers-Kronig relations. Furthermore, the brightness of the THz transients exceeds that of conventional thermal sources, and the gated detection is orders of magnitude more sensitive than bolometric detection. Recent developments have shown that THz-TDS has capabilities that go far beyond linear far-infrared spectroscopy. Because the THz transients are perfectly time-synchronized with the optical pulses that generate them, THz-TDS is ideally suited for "visible-pump, THz-probe" experiments. In