Since the publication of the seminal work of H. Federer which gives a rather complete and comprehensive discussion on the subject, the geometric measure theory has developed in the last three decades into an even more cohesive body of basic knowledge with an ample structure of its own, established strong ties with many other subject areas of mathematics and made numerous new striking applications. The present book is intended for the researchers in other fields of mathematics as well as graduate students for a quick overview on the subject of the geometric measure theory with emphases on various basic ideas, techniques and their applications in problems arising in the calculus of variations, geometrical analysis and nonlinear partial differential equations.

This graduate-level treatment of Geometric Measure Theory illustrates with concrete examples and emphasizes basic ideas and techniques with their applications to the calculus of variations, geometrical analysis, and non-linear PDEs.