Surgery theory is now about 40 years old. The 60th birthday (on
December 14, 1996) of C. T. C. Wall, one of the leaders of the founding
generation of the subject, led us to reflect on the extraordinary accomplish￾ments of surgery theory, and its current enormously varied interactions with
algebra, analysis, and geometry. Workers in many of these areas have of￾ten lamented the lack of a single source surveying surgery theory and its
applications. Indeed, no one person could write such a survey. Therefore
we attempted to make a rough division of the areas of current interest,
and asked a variety of experts to report on them. This is the first of two
volumes which are the result of that collective effort. We hope that they
prove useful to topologists, to other interested researchers, and to advanced
students