Some of the greatest advances in geometric combinatorics and harmonic analysis in recent years have been accomplished using the polynomial method. Larry Guth gives a readable and timely exposition of this important topic, which is destined to influence a variety of critical developments in combinatorics, harmonic analysis and other areas for many years to come. -Alex Iosevich, University of Rochester, author of The Erdos Distance Problem and A View from the Top. It is extremely challenging to present a current (and still very active) research area in a manner that a good mathematics undergraduate would be able to grasp after a reasonable effort, but the author is quite successful in this task, and this would be a book of value to both undergraduates and graduates. - Terence Tao, University of California, Los Angeles, author of An Epsilon of Room I, II and Hilbert's Fifth Problem and Related Topics In the 273 page long book, a huge number of concepts are presented, and many results concerning them are formulated and proved. The book is a perfect presentation of the theme. -Bela Uhrin, Mathematical Reviews