This volume carries the same title as that of an international conference held at the National University of Singapore, 9 11 January 2006 on the occasion of Roger E. Howe s 60th birthday. Authored by leading members of the Lie theory community, these contributions, expanded from invited lectures given at the conference, are a fitting tribute to the originality, depth and influence of Howe s mathematical work. The range and diversity of the topics will appeal to a broad audience of research mathematicians and graduate students interested in symmetry and its profound applications.