Fourier-transform infrared (FTIR) spectroscopy in high magnetic fields, concisely FTIR magneto-spectroscopy, is a powerful spectroscopic technique used to investigate many important effects in materials, e.g., electron paramagnetic resonance, cyclotron resonance, and transitions between Landau levels. Despite their enormous potential in solid-state physics, infrared magneto-spectrometers are still relatively rare and custom-made since such systems generally require complex infrastructure. This doctoral thesis describes in detail the design and implementation of a versatile FTIR magneto-spectroscopic setup operating in the range of 50 – 10 000 cm-1, high magnetic field up to 16 T and temperatures between 2 – 320 K located at the Central European Institute of Technology of Brno University of Technology. This setup allows us to perform a variety of magneto-optical measurements spanning the range from THz/far-infrared (FIR) to near-infrared (NIR). It consists of a commercial FTIR spectrometer coupled to a 16 T cryogen-free superconductive magnet by the custom-designed optical coupling and transmission probes designed for experiments with multiple detectors and samples in Faraday geometry. The novelty of the setup lies in the usage of a cryogen-free superconducting magnet. We have optimized and tested the performance of the FTIR magneto-spectroscopic setup for various configurations and determined a workable setup range. The functionality of the FTIR magneto-spectroscopic setup was demonstrated by the magneto-optical measurements of the zero-field splitting in cobalt(II)-based single ion magnet in the FIR region, indirect inter-band transitions between Landau levels (LLs) in germanium in the NIR region, and inter-band transitions between LLs in graphene in the FIR region.  Moreover, we measured the I-V characteristics of graphene bolometer devices.