Understanding the properties and physical phase of the dense strongly interacting matter present in the cores of neutron stars or created in their binary mergers remains one of the most prominent open problems in nuclear astrophysics. While most microscopic analyses have historically relied on solvable phenomenological models of nuclear and quark matter, in recent years a model-independent approach utilizing only controlled ,[object Object], calculations and astrophysical observations has emerged as a viable alternative.,[object Object],In these lecture notes, I review recent progress in first-principles weak-coupling calculations within high-density quark matter, shedding light on its thermodynamic and transport properties. I cover the most important technical tools used in such calculations, introduce selected highlight results, and explain how this information can be used in phenomenological studies of neutron-star physics. The notes do not offer a self-consistent treatment of the topics covered, but rather aim at filling gaps in existing textbooks on thermal field theory and at connecting the dots in a story developed in several recent research articles, to which the interested reader is directed for further technical details.