This book is the result of lecture courses on algebraic topology given by the author at the University of Manchester in 1967-1970,at Cornell University in 1970-1971 and at the Georg August University,Gottingen,in 1971-1972.The level of the material is more advanced than that of a first-year graduate course in algebraic topology;it is assumed that the student has already had a course on basic algebraic topology which included singular homology,the fundamental group and covering spaces.Moreover,a student who has never encountered differentiable manifolds will probably have difficulty with Chapter 12.On the other hand no knowledge of homotopy theory beyond the fundamental group is assumed.

Chapter 0 Some Facts from General Topology

Chapter 1 Categories,Functors and NaturalTransformations

Chapter 2 Homotopy Sets and Groups

Chapter 3 Properties of the Homotopy Groups

Chapter 4 Fibrations

Chapter 5 CW-Complexes

Chapter 6 Homotopy Properties of CW-Complexes

Chapter 7 Homology and Cohomology Theories

Chapter 8 Spectra

Chapter 9 Representation Theorems

Chapter 10 Ordinary Homology Theory

Chapter 11 Vector Bundles and K-Theory

Chapter 12 Manifolds and Bordism

Chapter 13 Products

Chapter 14 Orientation and Duality

Chapter 15 Spectral Sequences

Chapter 16 Characteristic Classes

Chapter 17 Cohomology Operations and Homology Cooperations

Chapter 18 The Steenrod Algebra and its Dual

Chapter 19 The Adams Spectral Sequence and the e-Invariant

Chapter 20 Calculation of the Cobordism Groups

Bibliography

Subject Index