In this volume, the state of the art in geodesy is presented with special emphasis on the challenges of the next decade. It is subdivided into six parts. The first five parts discuss the challenges of providing a stable global reference at the parts per billion level by space methods, the impact of recently approved dedicated satellite missions on the determination of a high resolution global gravity field and its refinements by airborne gravity, advances in geodynamics and their impact on the monitoring of seismic hazards and earthquake prediction, the increasing use of GPS and INS in kinematic mode for mapping the Earth's surface and monitoring the behaviour of large man-made structures, and the related advances in mathematical theory and numerical techniques. The last part is dedicated to the discussion of a new structure for IAG to meet these challenges.