The rudimentary concepts of thermodynamics are reviewed and further explored, after which advanced topics will be studied. Specifically, beginning with the postulation approaches, the physical structure of thermodynamics will be elucidated in a fundamental way. In contrast to conventional engineering approaches that are generally focused on the application aspects, we will discuss logic induction and the mathematical framework which shape this subject. In addition to some examples of relevance, regarding the formulation and description of fundamental equations, specific attention will be paid to advanced topics such as the stability of thermodynamic systems, phase transitions, and critical phenomena. Furthermore, closer insight will be gained as the macroscopic elements are connected to the microscopic structure, through the interpretation of entropy, in terms of a statistical mechanical treatment.