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The ESO workshop 'Multiple Stars across the H-R Diagram' was held in Garching on 12-15, July 2005. The topics included observations of multiple stars from ground and space, dynamical and stellar evolution in multiple systems, e?ects of the environment on multiplicity, formation and early e- lution of multiple stars, and special components of multiple stars (chemically peculiar stars, blue stragglers, brown dwarfs, etc.). Stars show a marked tendency to be in systems of di?erent multiplicity, 7 ranging from simple binaries and triples to globular clusters with N?10 . Modern observations give a frequency of binary and multiple stars in the Galactic ?eld of up to 70%, and between 5% and 20% of these systems are at least triple. There is evidence that the degree of multiplicity increases with primary mass. Many known multiple systems are too wide to have s- ni?cant physical interaction between their components. However, tidal and N-body dynamical interactions are important even in relatively wide s- tems and probably lead to the shrinkage of inner orbits. This sets the stage for spectacular evolutionary processes such as Roche-lobe over?ow, me- ers, supernovae, formation of special components, etc. Only recently did we realize that some of these processes require at least three stars. Theformationofmultiplesystemsremainsadi?cultandchallengingpart of astrophysics, although it has been addressed at the Workshop only brie?y.