Thermodynamics is a core part of science. Nearly all scientists should have a basic knowledge of thermodynamics. Thermodynamics is a science of development, and is a viewpoint of scientific development in natural sciences. Achievement of thermodynamics has influence not only on natural sciences, but also on social sciences and philosophy. Fundamental concepts and definitions are very important for any discipline of science, so what is classical thermodynamics and what is modern thermodynamics have become the key points of puzzledom in thermodynamics. In this paper, after clarification of fundamental concept in thermodynamics, a complete basic modern classification of thermodynamics is naturally obtained. It is suggested that extended Carnot theorem and dissipation decrease theorem, together with the laws of thermodynamics, are the most fundamental theorems in thermodynamics discipline. Nondissipative thermodynamics is a new field besides equilibrium thermodynamics belonging to the equal part of the second law of thermodynamics.