The authors present a summary of their many years of experience in teaching at a graduate level a new exposition of thermodynamics. It is an exposition of the thermodynamics of a new non-statistical paradigm of physics and thermodynamics, which applies to both large and small systems (including one particle systems) in any state: thermodynamic (i.e. stable) equilibrium or not. It uses as its primitives the concepts of inertial mass, force, and time and introduces the laws of thermodynamics in the most unambiguous and general formulations found in the literature. Starting with a precise definition of system and of state followed by statements and corollaries of the laws of thermodynamics, the thermodynamic formalism is developed without circularity and ambiguity. Definitions of energy, generalized available energy, and entropy apply to all states and follow (instead of precede) statements of the laws of thermodynamics. All other property definitions as well as those for the work, heat, and other interactions, which a system may have with its surroundings, follow from these statements and corollaries as well. In addition, fundamental and characteristic relations as well as interrelations relating property changes in going from one neighboring stable equilibrium state to the next are defined and developed for the students, while multidimensional surfaces relating energy, entropy, external parameters (e.g., volume, surface area, electric field strength, magnetic field strength, etc.), and amounts of constituents for all states (stable or not stable equilibrium) are used to assist the student in visually picturing the states of a system and the processes the system undergoes.An initial version of this paper was published inJuly of 2006 in the proceedings of ECOS’06, AghiaPelagia, Crete, Greece.