Quantum materials are a class of systems that host low energy emergent properties due to the strong correlations between the lattice, charge, spin and orbital degrees of freedom. In recent years, this classification has encompassed the world of strongly correlated materials, like high-temperature superconductors and Mott-Hubbard insulators, and the topological states of matter, like Dirac/Weyl semimetals and topological insulators. This doctoral thesis discusses the study of the optical characterization of novel quantum materials, with a special focus on the terahertz (THz) spectral range, where low energy emergent features arise as a consequence of strong electronic correlations, symmetry breaking and/or topological transitions. The low energy photons associated to THz radiation grant an easy access to the quasiparticles occupying the low energy modes of quantum materials. The recent progress in the generation and detection of THz radiation have enabled the production of ultrashort pulses at the picosecond scale and their exploitation in time-domain spectroscopy measurements, like pump-probe and nonlinear spectroscopy, from which it is possible to study the out-of-equilibrium dynamics of electrons and dipole-coupled low energy states, along with the appearance of nonlinear responses at the presence of high external electric fields. This thesis shows that quantum materials can host a plethora of THz-related responses which can be tuned in terms of their thickness, temperature and external drivings, like the perturbation associated to an ultrashort optical pulse. It addresses the optical and THz study of novel magnetic quantum materials like Co2MnGa, a magnetic nodal line semimetal, MnBi2Te4, the first intrinsic magnetic topological insulator discovered, and CrI3, a layered ferromagnetic insulator with research interests ranging from spintronics to topological Majorana modes. In particular, the interplay between the magnetic, electronic and phononic states is addressed through linear and nonlinear spectroscopy, along with the direct sampling of the topological features by optical means. As a final purpose, this thesis also reports the novel findings for the direct optical sampling of the superconductive gap in the Sr-doped nickelate NdNiO2, a strain-induced superconductor. The results show how the electrodynamic properties of this material are quantitatively different from the ones found in cuprate superconductors, sharing a similar infinite layer structural phase
