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"Hierarchical Classifications in Constraint Satisfaction (Third Edition)" defines a universal classification system for the instances of any finite Constraint Satisfaction Problem (CSP), the first level of which is their Trial-and-Error depth. It introduces two universal topologies on the set of instances of a CSP, for which all the classifications in the system are continuous; continuity expresses respectively invariance under expansion by Singles and monotonicity with respect to any expansion (two essential properties of any rational classification system). It analyses detailed classification and correlation results for the 9x9 Sudoku CSP. It also provides precise analyses of the various T&E kingdoms and it explores the ways of reaching and crossing their borders. It devotes a chapter to the specific questions raised by a recently discovered pattern (the tridagon) due to its exceptional persistency under "small" changes. A final chapter presents the four software tools that have been used for all the calculations in the book, so that the reader can easily reproduce and extend them.