This book aims at providing a solid basis for the education of the next generation of researchers in hot, dense QCD (Quantum ChromoDynamics) matter. This is a rapidly growing field at the interface of the smallest, i.e. subnuclear physics, and the largest scales, namely astrophysics and cosmology. The extensive lectures presented here are based on the material used at the training school of the European COST action THOR (Theory of hot matter in relativistic heavy-ion collisions). The book is divided in three parts covering ultrarelativistic heavy-ion collisions, several aspects related to QCD, and simulations of QCD and heavy-ion collisions. The scientific tools and methods discussed provide graduate students with the necessary skills to understand the structure of matter under extreme conditions of high densities, temperatures, and strong fields in the collapse of massive stars or a few microseconds after the big bang. In addition to the theory, the set of lectures presents hands-on material that includes an introduction to simulation programs for heavy-ion collisions, equations of state, and transport properties.