This book is based on lecture notes from a second-year graduate course, and is a greatly expanded version of our previous monograph K8]. We expose some aspects of the theory of semigroups of linear operators, mostly (but not only) from the point of view of its meeting with that part of spectral theory which is concerned with the integral representation of families of operators. This approach and selection of topics di?erentiate this book from others in the general area, and re?ect the author's own research directions. There is no attempt therefore to cover thoroughly the theory of semigroups...

This undergraduate textbook is based on lectures given by the author on the differential and integral calculus of functions of several real variables.