This volume includes both survey and research articles on major advances and future developments in geometry and topology. Papers include those presented as part of the 5th Aarhus Conference - a meeting of international participants held in connection with ICM Berlin in 1998 - and related papers on the subject. This collection of papers is aptly published in the ""Contemporary Mathematics"" series, as the works represent the state of research and address areas of future development in the area of manifold theory and geometry. The survey articles in particular would serve well as supplemental resources in related graduate courses.