The isomorphism problem for Coxeter groups
  By a recent result obtained by R. Howlett and the author considerable progress has been made towards a complete solution of the isomorphism problem for Coxeter groups. In this paper we give a survey on the isomorphism problem and explain in particular how the result mentioned above reduces it to its `reflection preserving' version. Furthermore we desrcibe recent developments concerning the solution of the latter. 
Bernhard M\"uhlherr