<P>This is a volume of research articles related to finite groups. Topics covered include the classification of finite simple groups, the theory of p-groups, cohomology of groups, representation theory and the theory of buildings and geometries.</P> <P>As well as more than twenty original papers on the latest developments, which will be of great interest to specialists, the volume contains several expository articles, from which students and non-experts can learn about the present state of knowledge and promising directions for further research.</P> <P>The Finite Groups 2003 conference was held in honor of John Thompson. The profound influence of his fundamental contributions is clearly visible in this collection of papers dedicated to him.</P>