The omnipresent augmented demand for revolutionary individual communication services at dramatically growing transmission rates has led to increasing the carrier frequencies from about 1 GHz to about 300 GHz and will require the progress towards quantum optical communications. Beginning with the discussion of communication and information in the quantum age, we carry over to the basics of quantum physics, like indeterminism, uncertainty and entanglement. All relevant fundamental mathematical concepts required for quantum communications and quantum computing, such as qubits, the Bloch sphere, teleportation, coherent and thermal states, quantum information, quantum channels and quantum noise, with detailed derivations and proves are included. The theoretical framework of quantum optical communications with quantum detection and estimation and culminating in innovative multipath transmission concepts is discussed, together with the detailed simulation concept. This textbook is especially made for electrical and information engineers and computer scientists, taking them by the hand and guiding them through the still somewhat obscured world of quantum optical communications which has been slowly discovered in engineering sciences.