Rudyak’s groundbreaking monograph is the first guide on the subject of cobordism since Stong's encyclopaedic and influential notes of a generation ago.

It concentrates on Thom spaces (spectra), orientability theory and (co)bordism theory, including (co)bordism with singularities.

Not only that, but Rudyak, of the University of Florida, USA, deals especially with Morava K-theories.

All of these diverse subjects are 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.

This same care makes the book easy to use by the student, for when proofs are not given, specific references are.

Presented here is the second, fully corrected print run of the first edition, published in 1998, which has become a standard reference text in algebraic topology.

In sum, this is a comprehensive yet user-friendly text on a subject of high importance in the world of mathematics.

From the reviews of the first edition: "…This is an important, formidable monograph…. The readers interested in pursuing this line of research wil