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Introduction PART 1. Preliminaries: Basic Homotopy Theory and Nilpotent Spaces Chapter 1. Cofibrations and fibrations Chapter 2. Homotopy colimits and homotopy limits; lim^1 Chapter 3. Nilpotent spaces and Postnikov towers Chapter 4. Detecting nilpotent groups and spaces PART 2. Localizations of Spaces at Sets of Primes Chapter 5. Localizations of nilpotent groups and spaces Chapter 6. Characterizations and properties of localizations Chapter 7. Fracture theorems for localization: groups Chapter 8. Fracture theorems for localization: spaces Chapter 9. Rational H-spaces and fracture theorems PART 3. Completions of Spaces at Sets of Primes Chapter 10. Completions of nilpotent groups and spaces Chapter 11. Characterizations and properties of completions Chapter 12. Fracture theorems for completion: groups Chapter 13. Fracture theorems for completion: spaces PART 4. An Introduction to Model Category Theory Chapter 14. An introduction to model category theory Chapter 15. Cofibrantly generated and proper model categories Chapter 16. Categorical perspectives on model categories Chapter 17. Model structures on the category of spaces Chapter 18. Model structures on categories of chain complexes Chapter 19. Resolution and localization model structures PART 5. Bialgebras and Hopf Algebras Chapter 20. Bialgebras and Hopf algebras Chapter 21. Connected and component Hopf algebras Chapter 22. Lie algebras and Hopf algebras in characteristic zero Chapter 23. Restricted Lie algebras and Hopf algebras in characteristic p Chapter 24. A primer on spectral sequences