Hernán Makse is Distinguished Professor of Physics and Neuroscience at the City University of New York, a member of the Memorial Sloan Kettering Cancer Center and founder of Kcore Analytics. He is Fellow of the American Physical Society and a member of the Brazilian Academy of Science. His research is focused on the understanding of biological, social and artificially intelligent systems. Paolo Boldi is Professor of Computer Science at the University of Milan. His research is focused on a wide range of topics including algorithms and data structures for big data, distributed systems and complex networks, and he has published over a hundred research articles in these areas. Francesco Sorrentino is Professor of Mechanical Engineering at the University of New Mexico. His is an expert in dynamical systems and control, with particular emphasis on nonlinear dynamics and optimal control. He has published more than 80 papers in international scientific peer reviewed journals and was the recipient of the National Institute of Health (NIH) Trailblazer Award from the National Institute of Biomedical Imaging and Bioengineering (NIBIB). Ian Stewart is Emeritus Professor of Mathematics at the University of Warwick and a Fellow of the Royal Society. He has six honorary degrees. His awards include the Michael Faraday Medal of the Royal Society, the Gold Medal of the IMA, and the Chancellor's Medal from the University of Warwick. He has published numerous successful books on various topics within mathematics.

• Preface; Part I. Symmetry Theory: Groups for Physics – Fibrations for Biology – Coverings for AI: 1. Biological symmetry; 2. Symmetry fibrations in a nutshell; 3. Graphs, networks, and synchronization; 4. Automorphisms and symmetry groups; 5. Input trees, synchrony, balanced colorings, and equitable partitions; 6. Graph fibration formalism; 7. Symmetry groupoid formalism; 8. Stability and synchronizability; 9. Extending fibrations from graphs to hypergraphs; 10. Fiber bundles for physics – fibrations for biology; 11. Symmetry and robustness in biological networks; 12. Geometrization of biology; 13. Software and algorithms to perform fibration analysis; Part II. Symmetry Application: From Gene Regulation to the Artificial Brain: 14. Fibration analysis of biological networks; 15. Simple fibration building blocks; 16. Fibration analysis of metabolic networks: complex building blocks; 17. Comparison between fibration building blocks, motifs and modules; 18. Synthetic biology through symmetries: the cell as a computer; 19. Taming biological complexity with symmetries: reducing the TRN to its minimal genome; 20. From structure to function: cluster synchronization in genetic networks; 21. All biology conspires against synchrony, so how can we be alive?; 22. From function to structure: network inference reconstruction; 23. Fibration theory of the brain I: C. elegans locomotion; 24. Fibration theory of the brain II: the minimal engram in mice; 25. Fibration theory of the brain III: the human language network; 26. Fibration deep learning; 27. Overview and outlook; References; Index.

Hernán Makse is Distinguished Professor of Physics and Neuroscience at the City University of New York, a member of the Memorial Sloan Kettering Cancer Center and founder of Kcore Analytics. He is Fellow of the American Physical Society and a member of the Brazilian Academy of Science. His research is focused on the understanding of biological, social and artificially intelligent systems. Paolo Boldi is Professor of Computer Science at the University of Milan. His research is focused on a wide range of topics including algorithms and data structures for big data, distributed systems and complex networks, and he has published over a hundred research articles in these areas. Francesco Sorrentino is Professor of Mechanical Engineering at the University of New Mexico. His is an expert in dynamical systems and control, with particular emphasis on nonlinear dynamics and optimal control. He has published more than 80 papers in international scientific peer reviewed journals and was the recipient of the National Institute of Health (NIH) Trailblazer Award from the National Institute of Biomedical Imaging and Bioengineering (NIBIB). Ian Stewart is Emeritus Professor of Mathematics at the University of Warwick and a Fellow of the Royal Society. He has six honorary degrees. His awards include the Michael Faraday Medal of the Royal Society, the Gold Medal of the IMA, and the Chancellor's Medal from the University of Warwick. He has published numerous successful books on various topics within mathematics.

• Preface; Part I. Symmetry Theory: Groups for Physics – Fibrations for Biology – Coverings for AI: 1. Biological symmetry; 2. Symmetry fibrations in a nutshell; 3. Graphs, networks, and synchronization; 4. Automorphisms and symmetry groups; 5. Input trees, synchrony, balanced colorings, and equitable partitions; 6. Graph fibration formalism; 7. Symmetry groupoid formalism; 8. Stability and synchronizability; 9. Extending fibrations from graphs to hypergraphs; 10. Fiber bundles for physics – fibrations for biology; 11. Symmetry and robustness in biological networks; 12. Geometrization of biology; 13. Software and algorithms to perform fibration analysis; Part II. Symmetry Application: From Gene Regulation to the Artificial Brain: 14. Fibration analysis of biological networks; 15. Simple fibration building blocks; 16. Fibration analysis of metabolic networks: complex building blocks; 17. Comparison between fibration building blocks, motifs and modules; 18. Synthetic biology through symmetries: the cell as a computer; 19. Taming biological complexity with symmetries: reducing the TRN to its minimal genome; 20. From structure to function: cluster synchronization in genetic networks; 21. All biology conspires against synchrony, so how can we be alive?; 22. From function to structure: network inference reconstruction; 23. Fibration theory of the brain I: C. elegans locomotion; 24. Fibration theory of the brain II: the minimal engram in mice; 25. Fibration theory of the brain III: the human language network; 26. Fibration deep learning; 27. Overview and outlook; References; Index.

Hernán Makse is Distinguished Professor of Physics and Neuroscience at the City University of New York, a member of the Memorial Sloan Kettering Cancer Center and founder of Kcore Analytics. He is Fellow of the American Physical Society and a member of the Brazilian Academy of Science. His research is focused on the understanding of biological, social and artificially intelligent systems. Paolo Boldi is Professor of Computer Science at the University of Milan. His research is focused on a wide range of topics including algorithms and data structures for big data, distributed systems and complex networks, and he has published over a hundred research articles in these areas. Francesco Sorrentino is Professor of Mechanical Engineering at the University of New Mexico. His is an expert in dynamical systems and control, with particular emphasis on nonlinear dynamics and optimal control. He has published more than 80 papers in international scientific peer reviewed journals and was the recipient of the National Institute of Health (NIH) Trailblazer Award from the National Institute of Biomedical Imaging and Bioengineering (NIBIB). Ian Stewart is Emeritus Professor of Mathematics at the University of Warwick and a Fellow of the Royal Society. He has six honorary degrees. His awards include the Michael Faraday Medal of the Royal Society, the Gold Medal of the IMA, and the Chancellor's Medal from the University of Warwick. He has published numerous successful books on various topics within mathematics.

• Preface; Part I. Symmetry Theory: Groups for Physics – Fibrations for Biology – Coverings for AI: 1. Biological symmetry; 2. Symmetry fibrations in a nutshell; 3. Graphs, networks, and synchronization; 4. Automorphisms and symmetry groups; 5. Input trees, synchrony, balanced colorings, and equitable partitions; 6. Graph fibration formalism; 7. Symmetry groupoid formalism; 8. Stability and synchronizability; 9. Extending fibrations from graphs to hypergraphs; 10. Fiber bundles for physics – fibrations for biology; 11. Symmetry and robustness in biological networks; 12. Geometrization of biology; 13. Software and algorithms to perform fibration analysis; Part II. Symmetry Application: From Gene Regulation to the Artificial Brain: 14. Fibration analysis of biological networks; 15. Simple fibration building blocks; 16. Fibration analysis of metabolic networks: complex building blocks; 17. Comparison between fibration building blocks, motifs and modules; 18. Synthetic biology through symmetries: the cell as a computer; 19. Taming biological complexity with symmetries: reducing the TRN to its minimal genome; 20. From structure to function: cluster synchronization in genetic networks; 21. All biology conspires against synchrony, so how can we be alive?; 22. From function to structure: network inference reconstruction; 23. Fibration theory of the brain I: C. elegans locomotion; 24. Fibration theory of the brain II: the minimal engram in mice; 25. Fibration theory of the brain III: the human language network; 26. Fibration deep learning; 27. Overview and outlook; References; Index.