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I am looking for a book that covers amenability rigorously. Preferably a book aimed at beginners.

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    $\begingroup$ Depending on what you want, Davidson's C$^*$-algebras by example or Wagon's The Banach-Tarski Paradox. $\endgroup$
    – Robert Furber
    Commented Feb 22, 2020 at 23:51
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    $\begingroup$ Appendix G on amenability of the book Kazhdan's Property (T) by Bekka, de la Harpe, Valette. $\endgroup$
    – YCor
    Commented Feb 23, 2020 at 9:33

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I suggest the book Amenability by Alan.t. Paterson. It contains everything about amenability of groups till the publication year 1988. But a newest one is Lectures on Amenability by Volker. Runde . It's main theme is about amenability of Banch Algebras.

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