ELA, Volume 12, p. 1, September 2004. PREFACE The Hamilton Institute at the National University of Ireland, Maynooth, is an Applied Mathematics research center whose activities span System Theory, Communication Networks, Machine Learning and Cognitive Neuroscience, Mathematical Biology and Human Computer Interaction. These areas of research require significant interdisciplinary interaction between engineers, computer scientists, physical scientists and mathematicians, and part of the remit of the Institute is to promote such cooperation. One of the mathematical disciplines that plays an important role in the research interests of the Hamilton Institute is Matrix Theory; in particular, the theory of Nonnegative Matrices. As part of this activity the Institute organized, with the support of the Science Foundation Ireland, a workshop on Nonnegative Matrices and their Applications that brought together matrix theorists and users of nonnegative matrices. The conference was held between July 11 and July 14, 2004, in Barberstown Castle and at the National University of Ireland, Maynooth. The organizing committee consisted of A. Berman, T. Laffey (chair), O. Mason, R. Shorten (Co. Chair) and F. Wirth. The program consisted of 29 talks given by speakers from Belgium, England, Germany, Ireland, Israel, Serbia, Taiwan and the United States. The past and present ILAS presidents, Hans Schneider, Richard Brualdi and Daniel Hershkowitz were the Workshop Banquet Speakers. The proceedings of the workshop are published in this volume of the Electronic Journal of Linear Algebra. All the articles in this volume went through the normal procedure of refereeing, according to the high standards of the journal. The workshop has already resulted in a number of collaborative projects between practitioners and mathematicians. and second Hamilton workshop on Nonnegative Matrices and their Applications in now currently being planned to further support and promote these activities. Abraham Berman and Thomas J. Laffey Special Editors