"Hierarchical Classifications in Constraint Satisfaction" starts by recalling the main universal classifications of the instances of a finite binary Constraint Satisfaction Problem, defined in previous books by the same author, as well as their first applications to the Sudoku case. It then introduces a software (SHC) specially developed by François Cordoliani to implement them in the Sudoku case. Finally, it analyses in detail the classification results thus obtained and it shows that the short SHC computation times suggest to use it in the ongoing search for the "hardest" puzzles.