New chapter devoted to Graph Property Testing and the included sections are Graph Property Testing; Testing Colorability; Szemeredi's Regularity Lemma; Testing Triangle-Freeness; and Characterizing the Testable Graph Properties. 

New sections have also been added on Percolation, Webgraphs, and Chernoff Bounds. 

A substantial revision has been made to the Double Jump section. 

The number of exercises included in the third edition has been almost doubled from that of the second edition, and hints and/or answers to some of the exercises are provided.