Hilbert’s fifth problem and related topics.
Terence Tao

Submitted for publication by the American Mathematical Society

Last updated: Nov 10, 2012

This continues my series of books derived from my blog, and is based on the lecture notes for my graduate course of the same name. The preceding books in this series were “Structure and Randomness“, “Poincaré’s legacies“, “An epsilon of room“, “An introduction to measure theory“, “Topics in random matrix theory“, “Higher order Fourier analysis“, and “Compactness and contradiction“.

A draft version of the MS can be found here.

Pre-errata (to be corrected in the published version):

• Page 5: In the proof of Theorem 1.1.2, $\varepsilon$ should be taken to be $1/10n$, rather than $1/10d$.
• Page 10: In Exercise 1.1.7, $(x+1,0)$ should be $(x+1,1)$, and $(x,1)$ should be $(x,0)$.
• Page 20: In Problem 1.1.14, the hypothesis that G has polynomial growth is missing and should be inserted.
• Page 79: In the last paragraph, a right parenthesis is missing after “Exercise 1.4.3″.

Thanks to Michael Cowling, Fan Zheng, and an anonymous contributor for corrections.