Greek mathematician Carathéodory published a work in 1909. in which, for the first time, the axiomatization of phenomenological thermodynamics was given. In the work, he brings a conceptual shift in the formulation of the second law of thermodynamics. His formulation does not rest upon the impossibility of some specific process or engine, but rather, he translates the second law of thermodynamics in a topological property of abstract state space. In this overview work, we formulate thermodynamics with Carathéodory’s main idea in mind. However, we do not formulate thermodynamics through rigorous mathematical formalism, but rather in a simple manner so we can show the main ideas of Carathéodory’s formulation. We give main ideas for setting up Carathéodory formulation and we show the importance of the relation of pre-order on state space and from it, we build the concept of empirical entropy. We show how Carathéodory’s formulation of the second law of thermodynamics is used in building up thermodynamics and we derive the standard claim that the entropy of isolated systems does not decrease