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Five main topics of computational plasticity are treated by experts in the field with latest research results, such as consistent linearizations and finite element techniques, the numerical analysis for stable volume-preserving time-integration at the plastic flow rule, the analysis and finite-element computation of shearband localizations and also of shake down load-factors for arbitrary non-linear kinematic hardening materials.The aim was primarely an integrated representation of the mathematical models, the analysis of numerical methods and the newest algorithms for the consistent and stable computation of large dimensional systems. The significance should be seen in the collection of textbook-like treatments of important new results from wellknown scientists.