This book presents the foundational physics underlying the generation of high intensity laser light and its interaction with matter. Comprehensive and rigorous, it describes how the strong electric and magnetic fields of a high intensity light pulse can shape the nonlinear dynamics of all forms of matter, from single electrons up to atomic clusters and plasmas. Key equations are derived from first principles and important results are clearly explained, providing readers with a firm understanding of the fundamental concepts that underlie modern strong field physics research. The text concludes with suggestions for further reading, along with an extensive reference list. Effective as both an educational resource and as a reference text, this book will be invaluable to graduates and researchers across the atomic, molecular and optical (AMO) and plasma physics communities.