There will be a two week workshop, June 7 - 18, 2004, on the topic: n-Categories: Foundations and Applications. This is the 2004 Summer Program of the Institute for Mathematics and its Applications, at the University of Minnesota. Further information may be found at: http://www.ima.umn.edu/categories Our main goal is to make progress in sorting out the basic foundational issues concerning definitions of "weak n-category", but the main areas of current and potential application will also be discussed. We have generous but limited funding from the IMA, and we have applied to the NSF for supplemental funding. Those interested are invited to register on-line at: http://www.ima.umn.edu/docs/reg_form1.html We will do the best that we can to find (partial) support. Graduate students and postdocs who are seriously interested in learning about this subject and who have some background in category theory and/or categorical homotopy theory are especially invited to register. John Baez and Peter May