Variational arguments are classical techniques whose use can be traced
back to the early development of the calculus of variations and further.
Rooted in the physical principle of least action they have wide
applications in diverse fields. This book provides a concise account of
the essential tools of infinite-dimensional first-order variational
analysis. These tools are illustrated by applications in many different
parts of analysis, optimization and approximation, dynamical systems,
mathematical economics and elsewhere. Much of the material in the book
grows out of talks and short lecture series given by the authors in the
past several years. Thus, chapters in this book can easily be arranged
to form material for a graduate level topics course. A sizeable
collection of suitable exercises is provided for this purpose. In
addition, this book is also a useful reference for researchers who use
variational techniques---or just think they might like to.