Texts and Readings in Mathematics

Based on lectures given by J.W. Milnor at Princeton in 1957, and written up by J.D. Stasheff a decade later, this book is widely recognised as a classic. It remains the best introduction to the algebraic topology of vector bundles, more specifically to the “characteristic classes” associated with the names of Euler, Steifel and Whitney, Chern, and Pontryagin. The book also contains a lovely treatment of Thom’s cobordism theory, and the Appendices give brisk accounts of singular homolgy and cohomology, as well as the Chern-Weil Theory.

Milnor was awarded the Fields Medal in 1962 and the Steele Prize for Mathematical Exposition in 2004. A part of the citation for the Steele Prize says:

The phrase sublime elegance is rarely associated with mathematical exposition, but it applies to all of Milnor’s writings, whether they be research or expository. Reading his books, one is struck with the ease with which the subject is unfolding, and it only becomes apparent after reflection that this ease is the mark of a master.