The purpose of this book is to provide a theoretical foundation and an understanding of atomistic spin-dynamics, and to give examples of where the atomistic Landau-Lifshitz-Gilbert equation can and should be used. The contents involve a description of density functional theory both from a fundamental viewpoint as well as a practical one, with several examples of how this theory can be used for the evaluation of ground state properties like spin and orbital moments, magnetic form-factors, magnetic anisotropy, Heisenberg exchange parameters, and the Gilbert damping parameter. This book also outlines how interatomic exchange interactions are relevant for the effective field used in the temporal evolution of atomistic spins. The equation of motion for atomistic spin-dynamics is derived starting from the quantum mechanical equation of motion of the spin-operator. It is shown that this lead to the atomistic Landau-Lifshitz-Gilbert equation, provided a Born-Oppenheimer-like approximation is made, where the motion of atomic spins is considered slower than that of the electrons. It is also described how finite temperature effects may enter the theory of atomistic spin-dynamics, via Langevin dynamics. Details of the practical implementation of the resulting stochastic differential equation are provided, and several examples illustrating the accuracy and importance of this method are given. Examples are given of how atomistic spin-dynamics reproduce experimental data of magnon dispersion of bulk and thin-film systems, the damping parameter, the formation of skyrmionic states, all-thermal switching motion, and ultrafast magnetization measurements.