The ESO workshop 'Multiple Stars across the H-R Diagram' was held in Garching on July 12-15, 2005. The topics included observations of multiple stars from ground and space, dynamical and stellar evolution in multiple systems, effects of the environment on multiplicity, formation and early evolution of multiple stars, and special components of multiple stars. Research on multiple stars has seen major developments during recent years due to the availability of large-aperture telescopes equipped with highly sophisticated instruments for multi-wavelength observations, of modern interferometers and of new satellites. The combination of results from satellites and ground-based facilities led to vivid interaction between the experts of all stellar type. The current state of observational and theoretical knowledge has been reviewed, and priorities for future studies have been discussed, so as to provide the necessary input for further progress in the understanding of the genesis of multiple stars, their structure and their role for the study of stellar evolution.