In six lectures aspects of modern non-equilibrium thermodynamics of discrete systems as well as continuum theoretical concepts are represented. Starting out with survey and introduction, state spaces are defined, the existence of internal energy is investigated, and Clausius inequality including negative absolute temperature is derived by diagram technique. Non-equilibrium contact quantities, such as contact temperature — the dynamic analogue of thermostatic temperature — and chemical potentials are phenomenologically defined and quantumstatistically founded. Using Clausius inequality the existence of non-negative entropy production is proved which allows to formulate a dissipation inequality in continuum thermodynamics. The transition between thermodynamics of discrete systems and continuum thermodynamics with respect to contact quantities is considered. Different possibilities of exploiting the dissipation inequality for getting constraints for constitutive equations are discussed. Finally hyperbolic heat conduction in non-extended thermodynamics is treated.Contents:IntroductionFirst LawSecond LawNon-Equilibrium Contact Quantities and their Quantum-Statistical FoundationExistence of Non-Negative Entropy ProductionContinuum ThermodynamicsReadership: Physicists, physico-chemists, theoretical engineers and thermodynamicists.Key Features:A very good and reliable guide for people interested in understanding the earlier stages of the Universe evolutionThe only example of a wide, but concise, study of both classical and quantum aspects of the UniverseAppropriate for experts in the field and as a handbook for preparing lectures; it also has all the characteristics of a textbook for undergraduate students and young researchersPresents topics from an objective point of view, highlighting pros and cons without prejudices, and animated by the natural curiosity towards new and intriguing arguments to model