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Based on a course given to beginning physics, chemistry, and engineering students at the Winterthur Polytechnic Institute, this text approaches the fundamentals of thermodynamics from the view of continuum mechanics. By describing physical processes in terms of the flow and balance of physical quantities, this provides a unified approach to hydraulics, electricity, mechanics and thermodynamics. In this way, it becomes clear that the entropy is the fundamental property that is transported in thermal process (what in lay terms would be called "heat"), and that the temperature is the corresponding potential. The resulting theory of the creation, flow, and balance of entropy provides the foundation of a dynamical theory of heat. Previous knowledge of thermodynamics is not required, but the reader should be familiar with basic electricity, mechanics, and chemistry and should have some knowledge of elementary calculus.