This thesis presents results of far-infrared spectroscopic studies of several low-temperature phenomena. Most of the experiments have been carried out in 401200 GHz range using a Mach-Zehnder interferometer. In addition to classical measurements of absorption, much attention has been put to the study of rotation of the polarization plane. Among investigated systems are two-dimensional electron gases (HgTe/CdHgTe quantum wells of critical thickness and GaAs/AlGaAs heterojunctions) and multiferroic dysprosium manganite. The electron band structure in HgTe/CdHgTe quantum wells is affected by a strong spin-orbit interaction in mercury telluride. According to theoretical calculations, the band structure takes a form close to a Dirac cone for a critical thickness (6.6 nm) of the HgTe layer. This prediction was experimentally confirmed by measurements of the cyclotron resonance. In external magnetic field the cyclotron resonance is seen as a dip in a transmission coefficient. Its position is determined by the cyclotron mass and its amplitude is connected to the charge density. The observed square-root dependence of the mass as a function of density provides a direct confirmation of the linear electron dispersion. Measurements of rotation of the polarization plane at 300 GHz allowed to observe the dynamic quantum Hall effect in the samples, in which the Fermi level is in the lower part of the Dirac cone. In high magnetic fields the Faraday rotation angle was found to demonstrate a quantized behavior, taking a value of the fine-structure constant (1/137). The Faraday angle is directly connected to the dynamic Hall conductivity, which is thus also quantized, showing the universal value e^2/h. The dynamic integer quantum Hall effect has been also studied in GaAs/AlGaAs heterojunctions. Quantization of the Hall conductivity has been detected below 100 GHz. Above this frequency the quantum plateaus are smeared out and replaced by small quantum oscillations in the real part of the conductivity. Similar oscillations were observed in the imaginary part as well. This effect has no analog at zero frequency, since the imaginary part is zero in the static case. The amplitude of the oscillations decreases with increasing frequency, and at 1 THz the Hall conductivity does not demonstrate any features related to the filling of Landau levels. This experimental picture is in partial agreement with analytical calculations for a delta-impurity limit and for a limit of a smooth potential, but in a disagreement with the results of numerical calculations for an intermediate case. Another interesting manifestation of the spin-orbit coupling has been demonstrated in a classical multiferroic manganite DyMnO3. In this material the microscopic spin-orbit interaction leads to a coupling between antiferromagnetic and ferroelectric orders. Because of intrinsic magnetoelectric coupling with electromagnons a linearly polarized terahertz light rotates upon passing through the sample. The amplitude and the direction of the polarization rotation are defined by the orientation of ferroelectric domains and can be changed by static voltage. These experiments allow the terahertz polarization to be electrically tuned using the dynamic magnetoelectric effect.