The paintings of Max Dehn (1878-1952) has been quietly influential in arithmetic because the starting of the twentieth century. In 1900 he grew to become the 1st to unravel one of many recognized Hilbert difficulties (the 3rd, at the decomposition of polyhedra), in 1907 he collaborated with Heegaard to provide the 1st survey of topology, and in 1910 he all started publishing his personal investigations in topology and combinatorial workforce idea. His effect is clear within the phrases Dehn's set of rules, Dehn's lemma and Dehn surgical procedure (and Dehnsche Gruppenbilder, quite often recognized in English as Cayley diagrams), yet direct entry to his paintings has been tricky. No version of his works has been produced, and a few of his most vital effects have been by no means released, at the least no longer through him. the current quantity is a modest try to convey Dehn's paintings to a much broader viewers, fairly topologists and crew theorists all for the origins in their topic and drawn to mining the assets for brand new rules. It comprises English translations of 8 works : 5 of Dehn's significant papers in topology and combinatorial workforce thought, and 3 unpublished works which remove darkness from the printed papers and include a few effects now not on hand somewhere else. furthermore, i've got written a brief creation to every paintings, summarising its contents and attempting to identify its position between similar works of Dehn and others, and i've extra an appendix at the Dehn-Nielsen theorem (often identified easily as Nielsen's theorem) .
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