This chapter reviews the basic tools of laser-plasma interaction theory. We start from Maxwell equations and Lorentz transformations for the electromagnetic (EM) field. Specific examples such as moving mirrors and an electron in a plane EM wave are described to get familiar with relativistic effects. Electrodynamics concepts such as light pressure, ponderomotive force and radiation friction are also described. The kinetic and fluid equations for collisionless plasmas are reviewed, with a justification for neglecting collisions. A brief survey of non-relativistic waves in plasmas is given, with a first glance at nonlinear effects such as the breaking of electrostatic plasma oscillations. For what concerns ion dynamics, the very basics of classic problems such as sheath formation, plasma expansion and collisionless shocks are given. Finally, a short introduction to numerical simulation methods is presented starting from the historical Dawson’s sheet model, focusing on the particle-in-cell (PIC) approach and including boosted frame techniques to save computational resources.