Introduction  
1 Part 1. Conservation of mass in Diffusion  
2 Study of the CM and its connections  
3 Breakdown of the paradigm for very fast diffusion, VFDE  
4 Mass conservation for the critical exponents  
5 What happened to the fundamental solutions  
6 Non-conservation in some borderline cases  
7 Part 2. Nonlinear fractional diffusion, NLFD  
8 Mass conservation in FPME  
9 Conservation of mass for FPLE. Critical case  
10 Part 3. Some related problems and open directions involving diffusion  