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In this paper, the foundations of classical phenomenological thermodynamics are being thoroughly revisited. A new rigorous basis for thermodynamics is laid out in the main text and presented in full detail in the appendix. All relevant concepts, such as work, heat, internal energy, heat reservoirs, reversibility, absolute temperature and entropy, are introduced on an abstract level and connected through traditional results, such as Carnot's Theorem, Clausius' Theorem and the Entropy Theorem. The paper offers insights into the basic assumptions one has to make in order to formally introduce a phenomenological thermodynamic theory. This contribution is of particular importance when applying phenomenological thermodynamics to systems, such as black holes, where the microscopic physics is not yet fully understood. Altogether, this work can serve as a basis for a complete and rigorous introduction to thermodynamics in an undergraduate course which follows the traditional lines as closely as possible.