Reflects recent developments related to the Monge-Ampere equation stressing the geometric aspects of the theory, using some techniques from harmonic analysis---covering lemmas and set decompositions. Essentially self-contained, the presentation unfolds systematically from introductory chapters, and an effort is made to present complete proofs of all theorems. Included are examples, illustrations, bibliographical references at the end of each chapter, and a comprehensive index. A concise and useful book for graduate students and researchers in the field of nonlinear equations.