For this course, advanced topics of thermodynamics will be studied and rudimentary concepts will be further explored. Starting with postulation approaches, the physical structure of thermodynamics shall be elucidated in a fundamental way. In contrast to conventional engineering approaches that are generally focused on the application aspects, we will discuss the logic induction and mathematical framework that shape this subject. In addition to the relevant examples, regarding the formulation and description of fundamental equations, specific interest will be directed to advanced topics such as stability of thermodynamic systems, phase transition, and critical phenomena. Furthermore, more insight shall be gained as the macroscopic elements are connected to the microscopic structure, through the interpretation of entropy, in terms of a statistical mechanical treatment.