  A short, tutorial introduction to some basic concepts of laser-plasma
interactions at ultra-high intensities is given. The selected topics include a)
elements of the relativistic dynamics of an electron in electromagnetic fields,
including the ponderomotive force and classical radiation friction; b) the
"relativistic" nonlinear optical transparency and self-focusing; c) the moving
mirror concept and its application to light sail acceleration and high harmonic
generation, with a note on related instabilities; d) some specific phenomena
related to the absorption of energy, kinetic momentum and angular momentum from
the laser light.
