In this tutorial paper we discuss the High Energy Transport (HETC)iLight Heavy Ion (LHI)/Spallation Gamma Source (SGS) Monte Carlo radiation transport computer code system, used to transport nucleons, pions, muons, photons, and "light heavy" nuclei with 2 < A < 10 through complex materials and geometries. In particular, we present for the first time in a single place a comprehensive, introductory discussion of HETC/LHI/SGS code physics.