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As far as I know, Riemann never left any books,

but after accidentally discovering 'on the hypotheses which lie at the bases of geometry' registered as Riemann's book on Google,

I began to wonder. Did Riemann leave any books?

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    $\begingroup$ By "leave", are you referring to posthumous publication? Ueber die Hypothesen, welche der Geometrie zu Grunde liegen. (1854) is Riemann's "Habilitationsschrift" (professorial dissertation) which was published posthumously in 1868. Interestingly enough, there seems to be a second "Habilitationsschrift" of his, Ueber die Darstellbarkeit einer Function durch eine trigonometrische Reihe (1854), likewise published in 1868. $\endgroup$
    – njuffa
    Commented Jun 3 at 0:25
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    $\begingroup$ Both of Riemann's professorial dissertations were not published as books, but are contained in volume 13 of Abhandlungen der Königlichen Gesellschaft der Wissenschaften in Göttingen (1868). "Ueber die Darstellbarkeit einer Function durch eine trigonometrische Reihe" appears on pp. 87-132, and ... $\endgroup$
    – njuffa
    Commented Jun 3 at 0:34
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    $\begingroup$ ... "Ueber die Hypothesen, welche der Geometrie zu Grunde liegen" appears on pp. 133-152. $\endgroup$
    – njuffa
    Commented Jun 3 at 0:35

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There is another book which has Riemann as an co-author:

Riemann and Weber, Die Partiellen Differentialgleichungen der Mathematischen Physik. Nach Riemann's Vorlesungen in vierter Auflage neu bearbeitet von HEINRICH WEBER, Professor der Mathematik an der Universitat Strassburg. Braunschweig, Friedrich Yieweg und Sohn. Erster Band, 1900, xvii + 506 pp. Zweiter Band, 1901, xi + 527 pp.

It was published by Weber, long time after Riemann's death, and is based on lectures of Riemann.

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  • $\begingroup$ @nuffia: yes, thanks, I corrected. $\endgroup$ Commented Jun 4 at 12:41
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A translation of Riemann's famous dissertation was published as a book:

Riemann, Bernhard. On the hypotheses which lie at the bases of geometry. Edited and with commentary by Jürgen Jost. Expanded English translation of the German original. Classic Texts in the Sciences. Birkhäuser/Springer, [Cham], 2016.

This is probably what influenced the Google perception that Riemann wrote a book.

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