Handbook of algebraic topology Algebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics. It is very much an international subject and this is reflected in the background of the 36 leading experts who have contributed to the Handbook. Written for the reader who already has a grounding in the subject the volume consists of 27 expository surveys covering the most active areas of research. They provide the researcher with an up to date overview of this exciting branch of mathematics Cover Contents Foreword List of Contributors Chapter 1. Homotopy types Chapter 2. Homotopy theories and model categories Chapter 3. Proper homotopy theory Chapter 4. Introduction to fibrewise homotopy theory Chapter 5. Coherent homotopy over a fixed space Chapter 6. Modem foundations for stable homotopy theory Chapter 7. Completions in algebra and topology Chapter 8. Equivariant stable homotopy theory Chapter 9. The stable homotopy theory of finite complexes Chapter 10. The EHP sequence and periodic homotopy Chapter 11. Introduction to nonconnective Im(J) theory Chapter 12. Applications of nonconnective Im(J) theory Chapter 13. Stable homotopy and iterated loop spaces Chapter 14. Stable operations in generalized cohomology Chapter 15. Unstable operations in generalized cohomology Chapter 16. Differential graded algebras in topology Chapter 17. Real and rational homotopy theory Chapter 18. Cohomology of groups Chapter 19. Homotopy theory of Lie groups Chapter 20. Computing v1 periodic homotopy groups of spheres and some compact Lie groups Chapter 21. Classifying spaces of compact Lie groups and finite loop spaces Chapter 22. H spaces with finiteness conditions Chapter 23. Co H spaces Chapter 24. Fibration and product decompositions in nonstable homotopy theory Chapter 25. Phantom maps Chapter 26. Walls finiteness obstruction Chapter 27. Lusternik Schnirelmann category Subject Index Last Page