The selected contributions in this volume originated at the Sundance conference, which was devoted to discussions of current work in the area of free resolutions. The papers include new research, not otherwise published, and expositions that develop current problems likely to influence future developments in the field.

Contributors -- Introduction -- Structure and Size of Free Resolutions -- Problems on infinite free resolutions -- /L. Avramov -- Problems on Betti numbers of finite length modules -- /H. Charalambous and E.G. Evans, Jr. -- Multiplicative structures on finite free resolutions -- /M. Miller -- Wonderful rings and awesome modules -- /G. Kempf -- Green's Conjecture -- Green's conjecture: an orientation for algebraists -- /D. Eisenbud -- Some matrices related to Green's conjecture -- /D. Bayer and M. Stillman -- Other Topics -- Problems on local cohomology -- /C. Huneke -- Recent work on Cremona transformations -- /S. Katz -- The homological conjectures -- /P. Roberts -- Remarks on residual intersections -- /B. Ulrich -- Some open problems in invariant theory -- /J. Weyman.