We discuss every principal permutation class that is generated by a pattern of length three or four. Upper and lower bounds for the challenging pattern 1324 have been improved several times since the last edition, and we included those results here. The spectacular proof by Adam Marcus and Gábor Tardos that affirmed the Stanley-Wilf conjecture is also included. This proof answers a question of Zoltán Füredi and Péter Hajnal on 0-1 matrices, and that answer implies that the size of every principal permutation class is at most https://www.w3.org/1998/Math/MathML"> c q n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429274107/76d8f3df-fdac-4af3-ad29-e5f6ca3c54a5/content/math00_6.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , where https://www.w3.org/1998/Math/MathML"> c q https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429274107/76d8f3df-fdac-4af3-ad29-e5f6ca3c54a5/content/math0_7.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> is a constant depending on the generator of the class. In this chapter, the exercises contain numerous new results.