This chapter reviews the perturbative renormalization of quantum chromodynamics (QCD), starting with an introduction to divergences in a simple scalar \(\phi ^4\) theory and the concept of the superficial degree of divergence. The analysis is extended to pure-glue Yang-Mills theory, suggesting its renormalizability. The main focus is the detailed one-loop renormalization of QCD using dimensional regularization, determining the necessary renormalization constants for the quark wave function, mass, gluon wave function, and the QCD vertex. Combining these constants proves the one-loop renormalizability of QCD. Finally, the chapter derives the one-loop running of the QCD coupling constant, demonstrating the property of asymptotic freedom which is the opposite behavior of the coupling in quantum electrodynamics.