After nearly half a century of developments in numerical methods, the field of computational mechanics has become sufficiently mature to collect the achievements and summarize the state-of-the-art in a comprehensive, authoritative major reference work. This idea, first conceived in 1999, has resulted in the Encyclopedia of Computational Mechanics. It has been the intention of the editors and the publisher to provide the community with a systematic, well-organized survey of established as well as recently developed computational methods, covering applied and computational mathematics, computer science, the various branches of solid and fluid mechanics, and all the available discretization methods. Attention has also been paid to many engineering and other applications.