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Today's complex cloud applications are composed of multiple components executed in multi-cloud environments. For such applications, the possibility to manage and control their cost, quality, and resource elasticity is of paramount importance. However, given that the cost of different services offered by cloud providers can vary a lot with their quality/performance, elasticity controllers must consider not only complex, multi-dimensional preferences and provisioning capabilities from stakeholders but also various runtime information regarding cloud applications and their execution environments. In this chapter, the authors present the elasticity control approach of the EU CELAR Project, which deals with multi-dimensional elasticity requirements and ensures multi-level elasticity control for fulfilling user requirements. They show the elasticity control mechanisms of the CELAR project, from application description to multi …