A Superintense Laser Plasma Interaction Theory Primer The continuous trend towards higher and higher laser intensities has opened the way to new physical regimes and advanced applications of laser plasma interactions thus stimulating novel connections with ultrafast optics astrophysics particle physics and biomedical applications. This book is primarily oriented towards students and young researchers who need to acquire rapidly a basic knowledge of this active and rapidly changing research field. To this aim the presentation is focused on a selection of basic models and inspiring examples and includes topics which emerged recently such as ion acceleration relativistic engineering and radiation friction. The contents are presented in a self contained way assuming only a basic knowledge of classical electrodynamics mechanics and relativistic dynamics at the undergraduate (Bachelor) level without requiring any previous knowledge of plasma physics. Hence the book may serve in several ways: as a compact textbook for lecture courses as a short and accessible introduction for the newcomer as a quick reference for the experienced researcher and also as an introduction to some nonlinear mathematical methods through examples of their application to laser plasma modeling