Learn the fundamentals of time-dependent density functional perturbation theory in this comprehensive 59-minute lecture by Stefano Baroni from Materials Cloud. Explore the theoretical foundations and mathematical framework of this advanced quantum mechanical method used to study the response of electronic systems to time-varying external perturbations. Discover how this approach extends traditional density functional theory to dynamic scenarios, enabling the calculation of excited-state properties, optical spectra, and electron-phonon interactions in materials. Gain insights into the linear response formalism, the role of exchange-correlation kernels, and practical applications in computational materials science. Master the key concepts that form the basis for understanding how materials respond to electromagnetic fields and other time-dependent perturbations at the quantum level.