* First, comprehensive, self contained textbook in the field of TDDFT, written by a leader in the field * The book has a strong emphasis on a pedagogical treatment, with many examples and 125 exercises. * Suitable as a textbook or companion book for graduate courses in electronic structure theory, theoretical spectroscopy, theoretical and computational chemistry, materials science and many other topics * The book presents an overview of the state of the art of the field of TDDFT, with over 800 references. * Many additional resources are contained in the appendices, including a long list of review literature and available computer codes. Time-dependent density-functional theory (TDDFT) describes the quantum dynamics of interacting electronic many-body systems formally exactly and in a practical and efficient manner. TDDFT has become the leading method for calculating excitation energies and optical properties of large molecules, with accuracies that rival traditional wave-function based methods, but at a fraction of the computational cost. This book is the first graduate-level text on the concepts and applications of TDDFT, including many examples and exercises, and extensive coverage of the literature. The book begins with a self-contained review of ground-state DFT, followed by a detailed and pedagogical treatment of the formal framework of TDDFT. It is explained how excitation energies can be calculated from linear-response TDDFT. Among the more advanced topics are time-dependent current-density-functional theory, orbital functionals, and many-body theory. Many applications are discussed, including molecular excitations, ultrafast and strong-field phenomena, excitons in solids, van der Waals interactions, nanoscale transport, and molecular dynamics. Table Of Contents 1: Introduction 2: Review of ground-state density-functional theory 3: Fundamental existence theorems 4: Time-dependent Kohn-Sham scheme 5: Time-dependent observables 6: Properties of the time-dependent xc potential 7: The formal framework of linear-response TDDFT 8: The frequency-dependent xc kernel 9: Applications in atomic and molecular systems 10: Time-dependent current-DFT 11: Time-dependent optimized effective potential 12: Extended systems 13: TDDFT and many-body theory 14: Long-range correlations and dispersion interactions 15: Nanoscale transport and molecular junctions 16: Strong-field phenomena and optimal control 17: Nuclear motion A: Atomic units B: Functionals and functional derivatives C: Densities and density matrices D: Hartree-Fock and other wave-function approaches E: Constructing the xc potential from a given density F: DFT for excited states G: Systems with noncollinear spin H: The dipole approximation I: A brief review of classical fluid dynamics J: Constructing the scalar from the tensor xc kernel K: Semiconductor quantum wells L: TDDFT in a Lagrangian frame M: Inversion of the dielectric matrix N: Review literature in DFT and many-body theory O: TDDFT computer codes