The paintings of Max Dehn (1878-1952) has been quietly influential in arithmetic because the starting of the twentieth century. In 1900 he turned the 1st to resolve one of many well-known Hilbert difficulties (the 3rd, at the decomposition of polyhedra), in 1907 he collaborated with Heegaard to supply the 1st survey of topology, and in 1910 he started publishing his personal investigations in topology and combinatorial workforce concept. His impression is obvious within the phrases Dehn's set of rules, Dehn's lemma and Dehn surgical procedure (and Dehnsche Gruppenbilder, in general recognized in English as Cayley diagrams), yet direct entry to his paintings has been tough. No variation of his works has been produced, and a few of his most vital effects have been by no means released, a minimum of now not through him. the current quantity is a modest try and deliver Dehn's paintings to a much wider viewers, quite topologists and team theorists thinking about the origins in their topic and drawn to mining the assets for brand spanking new principles. It involves English translations of 8 works : 5 of Dehn's significant papers in topology and combinatorial crew idea, and 3 unpublished works which light up the printed papers and comprise a few effects no longer to be had in other places. moreover, i've got written a quick creation to every paintings, summarising its contents and attempting to determine its position between similar works of Dehn and others, and i've additional an appendix at the Dehn-Nielsen theorem (often identified easily as Nielsen's theorem) .
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