This book is part of a four-volume set designed to provide students, engineers, and researchers with advanced knowledge for the design and development of architectured materials engineered to control radiative heat transfer in energy-related applications. The series is based on 14 written courses delivered during the CNRS thematic schoolMATTER(Architectured Materials for the Control of Radiative Heat Transfer: From Material Elaboration Processes to Industrial Applications), held from May 10&15, 2022, and organized by the French research network TAMARYS.This first volume introduces the fundamental principles of thermal radiation and provides a comprehensive overview of both classical and modern approaches to solving the Radiative Transfer Equation (RTE). Topics include heat exchange between opaque surfaces, the statistical foundations of radiative transfer, and simplified versions of the RTE useful for engineering applications. The book concludes with a detailed presentation of advanced numerical methods-both stochastic and deterministic-for solving the RTE accurately in complex semitransparent media.