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.