The aim of this book is to promote a fibrewise perspective, particularly in topology. Already this view is standard in the theory of fibre bundles and therefore in such subjects as global analysis. It has a role to play also in general and equivariant topology.
Stiefel manifolds are an interesting family of spaces much studied by algebraic topologists. These notes, which originated in a course given at Harvard University, describe the state of knowledge of the subject, as well as the outstanding problems. The emphasis throughout is on applications (within the subject) rather than on theory. However, such theory as is required is summarized and references to the literature are given, thus making the book accessible to non-specialists and particularly graduate students. Many examples are given and further problems suggested.
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