This graduate textbook introduces the com-putational techniques to study ultra-fast quantum dynamics of matter exposed to strong laser fields. Coverage includes methods to propagate wavefunctions according to the time dependent Schroedinger, Klein-Gordon or Dirac equation, the calculation of typical observables, time-dependent density functional theory, multi configurational time-dependent Hartree-Fock, time-dependent configuration interaction singles, the strong-field approximation, and the microscopic particle-in-cell approach. Contents How to propagate a wavefunction? Calculation of typical strong-field observables Time-dependent relativistic wave equations: Numerics of the Dirac and the Klein-Gordon equation Time-dependent density functional theory The multiconfiguration time-dependent Hartree-Fock method Time-dependent configuration interaction singles Strong-field approximation and quantum orbits Microscopic particle-in-cell approach

Due to the rapid progress in laser technology a wealth of novel fundamental and applied applications of lasers in atomic and plasma physics have become possible. This book focuses on the interaction of high intensity lasers with matter. It reviews the state of the art of high power laser sources, intensity laser-atom and laser-plasma interactions, laser matter interaction at relativistic intensities, and QED with intense lasers.