The work of Max Dehn (1878-1952) has been quietly influential in
mathematics since the beginning of the 20th century. In 1900 he became
the first to solve one of the famous Hilbert problems (the third, on the
decomposition of polyhedra), in 1907 he collaborated with Heegaard to
produce the first survey of topology, and in 1910 he began publishing
his own investigations in topology and combinatorial group theory. His
influence is apparent in the terms Dehn's algorithm, Dehn's lemma and
Dehn surgery (and Dehnsche Gruppenbilder, generally known in English as
Cayley diagrams), but direct access to his work has been difficult. No
edition of his works has been produced, and some of his most important
results were never published, at least not by him. The present volume is
a modest attempt to bring Dehn's work to a wider audience, particularly
topologists and group theorists curious about the origins of their
subject and interested in mining the sources for new ideas. It consists
of English translations of eight works: five of Dehn's major papers in
topology and combinatorial group theory, and three unpublished works
which illuminate the published papers and contain some results not
available elsewhere. In addition, I have written a short introduction to
each work, summarising its contents and trying to establish its place
among related works of Dehn and others, and I have added an appendix on
the Dehn-Nielsen theorem (often known simply as Nielsen's theorem) .
