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.From the reviews:pThis book maps the progress that has been made since the publication of the Ekeland variational principle in 1974 in the development and application of the variational approach in nonlinear analysis. The authors are well equipped for their task. a ] This monograph is distinctive for bringing out the unifying role of variational principles across nonlinear analysis, the numerous examples of their application, and for the insights communicated by the authors, drawing on their experience as key participants in their development. (Richard B. Vinter, Mathematical Reviews, Issue 2006 h)pThe book presents a nice treatment of known variational principles and their application in many fields of mathematics. a ] Many exercises are provided at the end of all sections where the reader can reflect the main text and can get further generalizations of the results. (JArg Thierfelder, Zentralblatt MATH, Vol. 1076, 2006)pThe aim of the book is to emphasize the strength of the variational techniques in various @P