The course is designed with students in mind who may be starting a PhD in quantum information. It assumes they have seen quantum theory before and some of the related maths. Nevertheless quantum theory is introduced from scratch including the differences between quantum and classical probability theory. The course aims to get the students to a point where they can begin to access the research literature. The formalism used for research (including the density matrix) is described. Key quantum information protocols and concepts are included, like teleportation, quantum key distribution and entanglement. Quantum entropy is defined and used for analyzing classical communication over quantum channels as well as quantum information thermodynamics. There is an emphasis on understanding the fundamental concepts and techniques.