Abstract: This talk will provide an overview of Terahertz (THz) spectroscopy as conducted in the Fahad Mahmood research group at the University of Illinois Urbana-Champaign (UIUC). THz spectroscopy serves as a powerful tool for probing and controlling optical responses in quantum materials by accessing low-energy excitations of electronic, lattice, and spin degrees of freedom. In the linear regime, we investigate how dipole oscillations, phonon-photon coupling, and free carrier dynamics contribute to material responses such as refractive index and absorption. The talk also highlights nonlinear optical phenomena enabled by intense THz fields, including second harmonic generation, THz emission, etc. These processes are governed by higher-order susceptibilities and are sensitive to the underlying crystal symmetries. Case studies such as Ca-doped SrTiO₃ and impulsive stimulated Raman scattering (ISRS) demonstrate how THz techniques can be used to probe and manipulate collective excitations.