The core of this book is variational methods and their applications in geometry, physics, mechanics engineering control and economics. The author set out to solve the classical and famous problems including Isoperimetric Problem, Brachistochrone Curve Problem, N-Body Problems, Geodesic Curve Problem, Minimal Surface Problem, Dirichlet Principle, Minimax Problems, Rabinowitz Minimal Period Conjecture, etc. The book contains many interesting historic backgrounds and important examples, explains profound theories in simple language, which can help readers to follow in order and advance step by step. The proofs for very difficult theorems are also clearly expressed, and all chapters and appendixes are very well-written. The book has 8 organized appendixes that are important and appropriate supplements to the main texts. Appendices 1 to 7 are related with some famous classical theorems while Appendix 8 is related with the famous Rabinowitz's minimum period conjecture. The level of this book is between the textbook for graduate students and monograph. The prerequisites on Calculus, Classical Mechanics, Ordinary Differential Equations and Real and Functional Analysis are required.

It is very useful for graduate students in mathematics, physics, mechanics and related engineering majors who want to improve their knowledge in Nonlinear Sciences. ". I find that it has a novel and interesting choice of topics, presented in a charming fashion." - Professor Francis H. Clarke, Claude Bernard University Lyon 1 ". It provides a thorough coverage of fundamental aspects the field and, in the later chapters, provides many significant areas application, which have not appeared previously in similar monographs." - Professor Richard B. Vinter, Imperial College London ".

I think this is a wonderful teaching level book for advanced undergraduates and graduate students. " - Professor Daniel C. Offin, Queen's University.