Introduction to Approximate Groups

My book Introduction to Approximate Groups (vol 94 of the London Mathematical Society Student Texts series, Cambridge University Press, 2020) is now available to read and buy online. Please note that it is under copyright and the pdf posted here is for personal, non-commercial use only, and may not be further distributed or posted elsewhere.

• Presents the fundamental properties of approximate groups, including a number that are known to experts but not easily accessible in the previous literature

• Streamlines and updates the exposition of various results, including my own classification of nilpotent approximate groups

• Features a substantial chapter on applications to geometric group theory, including growth, diameter bounds and isoperimetric inequalities

• Contains numerous exercises and motivating examples to help newcomers to the subject build their intuition and understanding

See also this review by Michael Björklund in Bull. Amer. Math. Soc..