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, Stiefel 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 homology and cohomology, as well as the Chern-Weil Theory.
