The objective of this project is to study the low energy electromagnetic response of topological mat- ter. To this end we will employ Terahertz time domain Faraday/Kerr spectroscopy in the frequency window from 0.5 - 4 THz to investigate the spectral properties of Dirac systems in the vicinity of the Fermi edge. Two main avenues will be pursued. One major direction will be the investigation of the low magnetic field magneto-optical response of three dimensional (3D) topological insulators (TI). For this class of materials symmetry considerations allow for the presence of an additional ∝ Θ E · B- term in Maxwells equations, which would give rise to a genuine magneto-electric response. While a quantized Faraday effect has been observed in high magnetic fields in 3D TIs, the direct observa- tion of a magneto-electric signal so far has kept elusive. We will launch a extended measurement campaign on 3D TIs to clearly answer the question whether or not a Θ-term is present. The sec- ond major direction will concentrate on the investigation of Dirac/Weyl systems. Here we will break new ground as experimental work on the low energy response of Weyl systems is currently lacking. The tremendous progress of crystal growth and post growth fabrication capabilities of HgTe based heterostructures provides us with direct access to well defined, high quality Weyl material with very low intrinsic carrier densities. Theoretical work suggests the presence of rich optical features in the energetic vicinity of the Dirac/Weyl point, which render these Weyl systems promising candidates for gyrotropic optical materials in the technologically very relevant Terahertz spectrum. As such materials are a prerequisite for optical technologies and do currently not exist in said regime, harnessing the optical properties of Weyl systems may be a route to close this technology gap.