What are the forms of energy at fundamental level?

Most high school textbooks distinguish several forms of energy.

1. 
   

   Mechanical:

   
   

   -Kinetic

   
   

   -Potential

   
   


2. Chemical



3. Electromagnetic


4. Nuclear


5. Gravitational


6. Thermal


7. Hydraulic


8. Electric


9. Mass


10. ...

This classification is probably unnecessary and arbitrary (like differentiating the gravity of alive and inert bodies).

I think that at least we could reduce the list to mechanical, electromagnetic, nuclear (weak and strong), mass and gravitational energy. In QFT mechanical energy might disappear.

Are the other important types? Does this classification make any sense at fundamental level?