Algebraic Topology - Homotopy and Homology

Biography of Robert M. Switzer

0 Some Facts from General Topology.- 1 Categories, Functors and Natural Transformations.- 2 Homotopy Sets and Groups.- 3 Properties of the Homotopy Groups.- 4 Fibrations.- 5 CW-Complexes.- 6 Homotopy Properties of CW-Complexes.- 7 Homology and Cohomology Theories.- 8 Spectra.- 9 Representation Theorems.- 10 Ordinary Homology Theory.- 11 Vector Bundles and K-Theory.- 12 Manifolds and Bordism.- 13 Products.- 14 Orientation and Duality.- 15 Spectral Sequences.- 16 Characteristic Classes.- 17 Cohomology Operations and Homology Cooperations.- 18 The Steenrod Algebra and its Dual.- 19 The Adamss Spectral Sequence and the e-Invariant.- 20 Calculation of the Cobordism Groups.

From the reviews:

"This book contains much impressive mathematics, namely the achievements by algebraic topologists in obtaining extensive information on the stable homotopy groups of spheres, and the computation of various cobordism groups. It is a long book, and for the major part a very advanced book. ... (It is) suitable for specialists, or for those who already know what algebraic topology is for, and want a guide to the principal methods of stable homotopy theory."
R. Brown in Bulletin of the London Mathematical Society, 1980

"In the more than twenty five years since its first appearance, the book has met with favorable response, both in its use as a text and as reference. It is a good course which leads the reader systematically to the point at which he can begin to tackle problems in algebraic topology. ... This book remains one of the best sources for the material which every young algebraic topologist should know." (Corina Mohorianu, Zentralblatt MATH, Vol. 1003 (3), 2003)