Rudyak's groundbreaking monograph is the first guide on the subject of cobordism since Stong's influential notes of a generation ago. It concentrates on Thom spaces (spectra), orientability theory and (co)bordism theory (including (co)bordism with singularities and, in particular, Morava K-theories). These are all framed by (co)homology theories and spectra. The author has also performed a service to the history of science in this book, giving detailed attributions.

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From the reviews of the first printing:

"... This is an important, formidable monograph in the area of algebraic and geometric topology. The readers interested in pursuing this line of research will find it enormously helpful to have the results assembled in one place with an unified, brilliant exposition."

C.Costinescu, Zentralblatt Math 906.1999

"This book provides an excellent and thorough treatment of various topics related to cobordosm. It should become an indispensable tool for advanced graduate students and workers in algebraic topology. ..."

D.M.Davis, MathSciNet MR1627486 (99f:550001)

".... The book is indispensable for research workers in algebraic topology. The presentation of the material is very nice and thorough, and this makes the book convenient for students with preliminary knowledge of algebraic topology. ..."

EMS - European Mathematical Society Newsletter December 1999

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