A method for studying the time-dependent electronic state of a given many-electron system within the framework of the density functional theory. While the conventional (static) density functional theory is based on the fact that the ground state energy can be characterized by some functional of the density, the TDDFT is based on its extension to time-dependent density (Runge-Gross theorem). It is possible to obtain the time-dependence of the electronic state of molecules and solids by solving the equation derived from the theorem. Often used in studying the non-linear response to the strong external field. Supported by many standard packages of the first principle calculation and quantum chemistry such as VASP, CASTEP, ABNINT, QUANTUM ESPRESSO, PHASE, Gaussian, GAMESS-US, etc.